2407.04973

# LogicVista: Multimodal LLM Logical Reasoning Benchmark in Visual Contexts Abstract We propose LogicVista, an evaluation benchmark that assesses the integrated logical reasoning capabilities of multimodal large language models (MLLMs) in Vis ual contexts. Recent advancements in MLLMs have demonstrated various fascinating abilities, from crafting poetry based on an image to performing mathematical reasoning. However, there is still a lack of systematic evaluation of MLLMs’ proficiency in logical reasoning tasks, which are essential for activities like navigation and puzzle-solving. Thus we evaluate general logical cognition abilities across 5 logical reasoning tasks encompassing 9 different capabilities, using a sample of 448 multiple-choice questions. Each question is annotated with the correct answer and the human-written reasoning behind the selection, enabling both open-ended and multiple-choice evaluation. A total of 8 MLLMs are comprehensively evaluated using LogicVista. Code and Data Available at https://github.com/Yijia-Xiao/LogicVista. ∗ Both authors contributed equally. 1 Introduction Recent advancements in Large Language Models (LLMs) are gradually turning the vision of a generalist AI agent into reality. These models exhibit near-human expert-level performance across a variety of tasks and have recently been augmented with visual understanding capabilities, enabling them to tackle even more complex visual challenges. This branch of work, led by proprietary projects such as GPT-4 [1] and Flamingo [2], as well as open-source efforts like LLaVA [3], Mini-GPT4 [4], enhances existing LLMs by incorporating visual comprehension. These models, known as Multimodal Large Language Models (MLLMs), use LLMs as the foundation for processing information and generating reasoned outcomes [5], thereby bridging the gap between language and vision. Recent MLLMs have demonstrated a range of impressive abilities, such as writing poems based on an image [6], engaging in mathematical reasoning [2], and even aiding in medical diagnosis [7]. To evaluate the performance of these models, various benchmarks have been proposed, as shown in Figure. 1 targeting the performance on common tasks such as objects recognition [8], text understanding in images [9], or mathematical problem solving [10]. However, as seen in Figure. 1, there is a notable shortage of benchmarks for MLLMs’ abilities in critical logical reasoning tasks that underlie most tasks. Perception and reasoning are two representative abilities of high-level intelligence that are used in unison during human problem-solving processes. Many current MLLM datasets have focused solely on perception tasks, which require fact retrieval where the MLLM identifies and retrieve relevant information from a scene. However, complex multimodal reasoning, such as interpreting graphs [11], everyday reasoning, critical thinking, and problem-solving [12, 13] requires a combination of perception and logical reasoning. Proficiency in these reasoning skills is a reliable indicator of cognitive capabilities required for performing specialized or routine tasks across different domains. To our knowledge, MathVista [14] is the only benchmark that attempts to evaluate multimodal logical reasoning, but its scope is limited to mathematical-related reasoning. For a better understanding of how MLLMs perform on general reasoning tasks, there is a need for a comprehensive and general visual reasoning benchmark. | LogicVista (Ours) | | | | | | | | | VQAv2, TextVQA and MM-vet | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | <details> <summary>extracted/5714025/figures/ours1.png Details</summary>  ### Visual Description ## Diagram: Geometric Configurations with Diagonal and Vertical Lines ### Overview The image contains 10 labeled diagrams (A-E, repeated twice) arranged in two rows. Each diagram features a square divided by a diagonal line and a vertical line. The diagrams vary in the position of the vertical line (left, middle, right) and the orientation of the diagonal line (top-left to bottom-right or top-right to bottom-left). Black squares are positioned in specific corners relative to the lines. ### Components/Axes - **Diagrams**: Labeled A to E (each repeated once). - **Square**: Uniformly sized, divided into regions by: - **Diagonal Line**: Connects two opposite corners (either top-left to bottom-right or top-right to bottom-left). - **Vertical Line**: Splits the square into left and right regions; position varies (left, middle, right). - **Black Square**: Placed in one corner of the larger square, overlapping with the intersection of the diagonal and vertical lines in some cases. ### Detailed Analysis 1. **Diagram A**: - Vertical line on the left. - Diagonal line from top-left to bottom-right. - Black square in the bottom-left corner. 2. **Diagram B**: - Vertical line in the middle. - Diagonal line from top-left to bottom-right. - Black square in the bottom-left corner. 3. **Diagram C**: - Vertical line on the right. - Diagonal line from top-left to bottom-right. - Black square in the bottom-right corner. 4. **Diagram D**: - Vertical line in the middle. - Diagonal line from top-right to bottom-left. - Black square in the top-right corner. 5. **Diagram E**: - Vertical line on the left. - Diagonal line from top-right to bottom-left. - Black square in the top-left corner. ### Key Observations - **Vertical Line Position**: Alternates between left, middle, and right across diagrams. - **Diagonal Orientation**: Alternates between two orientations (top-left to bottom-right vs. top-right to bottom-left). - **Black Square Placement**: Positioned to align with the intersection of the diagonal and vertical lines in most cases (e.g., bottom-left in A/B, bottom-right in C, top-right in D, top-left in E). ### Interpretation The diagrams likely illustrate scenarios where the intersection of two decision boundaries (diagonal and vertical lines) determines an outcome (represented by the black square). For example: - **Decision Trees**: The vertical line could represent a binary choice (left/right), while the diagonal line represents a secondary condition (e.g., cost vs. benefit). - **Resource Allocation**: The black square might symbolize an optimal resource distribution point based on two constraints. - **Game Theory**: The configurations could model strategies where players choose between options (vertical line) and outcomes (diagonal line). No numerical data or trends are present. The diagrams emphasize spatial relationships and positional logic rather than quantitative analysis. </details> | Q: Which of the boxes comes next? A: E Reasoning Skill: Inductive Capability: Diagram | <details> <summary>extracted/5714025/figures/vqav2.jpg Details</summary>  ### Visual Description ## Photograph: Tennis Player in Action ### Overview The image captures a dynamic moment of a female tennis player executing a forehand stroke on a hard court. The player is mid-motion, with her body leaning forward, right arm extended to strike a yellow tennis ball, and left arm outstretched for balance. The scene is set outdoors under bright sunlight, with a chain-link fence and sparse vegetation visible in the background. ### Components/Axes - **Subject**: Female tennis player (center-right of frame). - **Court**: Green hard court with white boundary lines (visible at the bottom of the image). - **Background**: Chain-link fence (occupying ~70% of the upper frame), with blurred trees and shrubs. - **Lighting**: Bright daylight, casting sharp shadows on the court. ### Detailed Analysis - **Player Attire**: - Red short-sleeve shirt with a white circular logo (resembling a flame or sun) and the text "WILD" beneath it. - White tennis skirt and white athletic shoes. - White visor with a logo (text indiscernible). - **Ball**: Yellow tennis ball in mid-air, positioned ~15 cm above the player’s racket. - **Racket**: Blue and white tennis racket held in the player’s right hand, angled toward the ball. - **Motion**: Player’s right leg is lifted mid-stride, left foot planted on the court. ### Key Observations 1. **Ball Trajectory**: The ball is slightly ahead of the racket, suggesting a forehand stroke in progress. 2. **Player Focus**: Eyes locked on the ball, indicating concentration. 3. **Environment**: No spectators or opponents visible; isolated action shot. 4. **Lighting**: High contrast between the player’s red shirt and the green court. ### Interpretation The image emphasizes athleticism and precision, capturing the split-second coordination required in tennis. The player’s posture and ball positioning suggest a powerful forehand stroke, likely during a rally. The absence of opponents or audience implies this could be a practice session or a drill. The "WILD" logo on the shirt may indicate a team, sponsor, or brand affiliation, though no further context is provided. No numerical data, charts, or diagrams are present. The textual elements are limited to the "WILD" logo and potential logos on the visor (unreadable). </details> | Q: Is the girl touching the ground? A: No Reasoning Skill: None Capability: Recognition | | --- | --- | --- | --- | | <details> <summary>extracted/5714025/figures/ours2.png Details</summary>  ### Visual Description ## Diagram: 3D Cube Structure with 2D Partitioned Views ### Overview The image depicts a 3D geometric structure resembling a cube with a smaller cube attached to its top face and a cutout section on one side. Below the 3D structure, four 2D diagrams (labeled A, B, C, D) are arranged in a 2x2 grid. Each diagram shows a square partitioned into irregular regions with varying configurations. ### Components/Axes - **3D Structure**: - A cube with a smaller cube stacked on its top face. - A rectangular cutout on the front face, creating an open cavity. - No explicit labels, axes, or legends are present in the 3D structure. - **2D Diagrams (A, B, C, D)**: - **Diagram A**: A square divided into three regions: a small square in the top-left, a horizontal rectangle spanning the bottom half, and a vertical rectangle on the right. - **Diagram B**: A square partitioned into four regions: a small square in the top-left, a horizontal rectangle in the top-right, a vertical rectangle in the bottom-left, and a larger square in the bottom-right. - **Diagram C**: A square divided into four regions: a small square in the bottom-left, a horizontal rectangle spanning the top half, a vertical rectangle on the right, and a larger square in the bottom-right. - **Diagram D**: A square divided into four equal smaller squares (2x2 grid). ### Detailed Analysis - **3D Structure**: - The cube’s orientation suggests a perspective view, with the cutout revealing internal depth. - The smaller cube on top creates a stepped effect, emphasizing vertical layering. - **2D Diagrams**: - **Diagram A**: Asymmetrical partitioning with uneven regions. - **Diagram B**: Balanced but irregular partitioning, with one large square dominating the bottom-right. - **Diagram C**: Similar to B but with the small square shifted to the bottom-left. - **Diagram D**: Uniform partitioning into equal quadrants. ### Key Observations 1. The 3D cube’s complexity contrasts with the simplicity of the 2D diagrams. 2. Diagrams A, B, and C share a recurring pattern of a small square and a large square, while D is uniform. 3. No numerical values, legends, or axis markers are present in any diagram. ### Interpretation The image likely illustrates a conceptual relationship between 3D spatial reasoning and 2D representation. The 3D cube’s cutout and layered structure may symbolize fragmentation or modularity, while the 2D diagrams could represent different ways to partition or analyze a system. Diagram D’s uniformity might signify standardization, whereas A, B, and C highlight variability in segmentation. The absence of labels suggests the focus is on visual patterns rather than quantitative data. ## No textual data, numerical values, or legends are present in the image. The analysis is based solely on geometric and spatial relationships. </details> | Q: Which of these are the top view? A: B Reasoning Skill: Spatial Capability: 3D Shape | <details> <summary>extracted/5714025/figures/textvqa.jpg Details</summary>  ### Visual Description ## Digital Transit Display: Route Information ### Overview The image shows a digital display sign with a black background, featuring three rows of text in white and yellow. The display uses a grid-based font with green rectangular blocks separating text segments. The content indicates a transit route with origin, next stop, and destination information. ### Components/Axes - **Text Elements**: - **ORIGIN:** (White text, top-left) - **NEXT STOP:** (White text, middle-left) - **DESTINATION:** (White text, bottom-left) - **Location Labels**: - **WASHINGTON** (Yellow text, aligned with "ORIGIN:") - **BWI AIRPORT** (Yellow text, aligned with "NEXT STOP:") - **NEW YORK** (Yellow text, aligned with "DESTINATION:") - **Design Elements**: - Green rectangular blocks (4 per row) separating text segments - Black background with no additional graphics ### Detailed Analysis 1. **ORIGIN:** - Text: "WASHINGTON" (Yellow, 7-character grid font) - Position: Top row, left-aligned - Green blocks: 4 blocks after "WASHINGTON" 2. **NEXT STOP:** - Text: "BWI AIRPORT" (Yellow, 11-character grid font) - Position: Middle row, left-aligned - Green blocks: 4 blocks after "BWI AIRPORT" 3. **DESTINATION:** - Text: "NEW YORK" (Yellow, 8-character grid font) - Position: Bottom row, left-aligned - Green blocks: 4 blocks after "NEW YORK" ### Key Observations - All text uses a consistent grid-based font with uniform spacing - Yellow text contrasts sharply against the black background - Green blocks serve as visual separators but lack explicit legend explanation - No numerical data, timestamps, or additional UI elements visible - Text alignment is strictly left-justified across all rows ### Interpretation This display functions as a real-time transit information system, likely for trains or buses. The structure suggests: 1. **Origin**: Current location (Washington) 2. **Next Stop**: Immediate destination (BWI Airport) 3. **Destination**: Final endpoint (New York) The use of color coding (yellow text, green blocks) enhances readability in transit environments. The absence of timestamps or additional metrics implies this is a static route display rather than a dynamic schedule. The green blocks may indicate progress markers or simply serve as visual dividers. The route appears to be a through-service connecting Washington to New York via BWI Airport, suggesting a multi-modal transit system. </details> | Q: What is the final destination? A: New York Reasoning Skill: None Capability: OCR | | <details> <summary>extracted/5714025/figures/ours3.png Details</summary>  ### Visual Description ## Diagram: Balance Scale with Torque Equilibrium ### Overview The image depicts a horizontal balance scale with three weights positioned at varying distances from the fulcrum (center pivot point). The system is in static equilibrium, with the beam balanced horizontally. ### Components/Axes - **Fulcrum**: Central pivot point (orange triangle) labeled with a dashed vertical line. - **Weights**: - Left side: - 20 lb weight positioned 6 ft left of the fulcrum. - 30 lb weight positioned 3 ft left of the fulcrum. - Right side: - Unknown weight (marked with "?") positioned 6 ft right of the fulcrum. - **Distances**: - Arrows indicate distances from the fulcrum: 6 ft (left and right), 3 ft (left). ### Detailed Analysis 1. **Torque Calculation**: - Left side total torque: $ (20 \, \text{lb} \times 6 \, \text{ft}) + (30 \, \text{lb} \times 3 \, \text{ft}) = 120 \, \text{lb-ft} + 90 \, \text{lb-ft} = 210 \, \text{lb-ft} $. - Right side torque must equal 210 lb-ft for equilibrium. - Unknown weight: $ \frac{210 \, \text{lb-ft}}{6 \, \text{ft}} = 35 \, \text{lb} $. 2. **Spatial Grounding**: - All weights are aligned horizontally along the beam. - Distances are explicitly labeled with arrows pointing to the fulcrum. ### Key Observations - The system adheres to the principle of torque equilibrium: $ \text{Torque}_{\text{left}} = \text{Torque}_{\text{right}} $. - The unknown weight is calculated to be **35 lb** to maintain balance. - No outliers or anomalies; the diagram explicitly shows a balanced state. ### Interpretation This diagram demonstrates the application of rotational equilibrium in physics. The placement and magnitude of weights are inversely proportional to their distances from the fulcrum to achieve balance. The calculation confirms that the unknown weight must be **35 lb** to counteract the combined torque of the left-side weights. The diagram serves as a visual aid for understanding lever mechanics and torque distribution. </details> | Q: What is the weight if balanced? A: C: 35 lb Reasoning Skill: Mechanical Capability: Physics | <details> <summary>extracted/5714025/figures/mmvet1.png Details</summary>  ### Visual Description ## Photograph: Children Solving Math Problems on a Chalkboard ### Overview The image depicts three children (two girls and one boy) from behind, actively writing on a dark green chalkboard. Each child is solving a basic arithmetic problem using white chalk. The chalkboard contains three incomplete equations: 1. `3×3=` (left side) 2. `7×2=` (center) 3. `11-2=` (right side) The children are wearing school uniforms: navy-blue vests with red trim over white shirts. Their hair is tied back with clips (red, yellow, and purple). The chalkboard shows faint erasure marks, suggesting prior use. ### Components/Axes - **Chalkboard**: Dark green surface with white chalk markings. - **Text**: Three arithmetic problems (`3×3=`, `7×2=`, `11-2=`). - **Subjects**: Three children (two girls, one boy) positioned left-to-right. ### Detailed Analysis 1. **Left Child (Girl)**: - Wearing a red hair clip. - Writing `3×3=`; no answer provided. - Uniform: Navy vest with red trim, white shirt. 2. **Center Child (Girl)**: - Hair tied with yellow and purple clips. - Writing `7×2=`; no answer provided. - Uniform: Navy vest with red trim, white shirt with pink collar. 3. **Right Child (Boy)**: - Short, dark hair. - Writing `11-2=`; no answer provided. - Uniform: Navy vest with red trim, white shirt. ### Key Observations - All equations are incomplete; no solutions are written. - Children are focused on their tasks, suggesting a learning activity. - Uniforms indicate a formal educational setting (e.g., classroom). - Chalkboard shows signs of prior use (faint erasure marks). ### Interpretation The image captures a moment of active learning, emphasizing foundational math skills (multiplication and subtraction). The absence of answers suggests the children are in the process of solving problems, possibly during a lesson or exercise. The uniformity in attire and the structured activity imply a disciplined educational environment. The chalkboard’s wear indicates repeated use, reinforcing the idea of a classroom setting. No numerical data or trends are present beyond the arithmetic problems. The image prioritizes visual storytelling over quantitative analysis. </details> | Q: What will girl on right write? A: 14 Reasoning Skill: Numerical Capability: OCR | Figure 1: Capabilities and reasoning skills of various existing benchmarks. Traditional benchmarks seldom assess reasoning skills, whereas LogicVista emphasizes the fundamental capacities necessary for solving specific problems, going beyond simple recognition or math tasks. We argue that a universal comprehensive evaluation benchmark should have the following characteristics: (1) cover a wide range of logical reasoning tasks, including deductive, inductive, numeric, spatial, and mechanical reasoning; (2) present information in both graphical and Optical Character Recognition (OCR) formats to accommodate different types of data inputs; and (3) facilitate convenient quantitative analysis for rigorous assessment and comparison of model performance. To this end, we present a comprehensive MLLM evaluation benchmark, named LogicVista, which meets all these criteria: - LogicVista covers 5 representative categories of logical reasoning tasks: inductive ( $sample=107$ ), deductive ( $sample=93$ ), numerical ( $sample=95$ ), spatial ( $sample=79$ ), and mechanical ( $sample=74$ ). - LogicVista includes a variety of capabilities, ranging from diagrams ( $sample=330$ ), OCR, ( $sample=234$ ), patterns ( $sample=105$ ), graphs ( $sample=67$ ), tables ( $sample=70$ ), 3D shapes ( $samples=45$ ), puzzles ( $samples=256$ ), sequences ( $samples=76$ ), and physics ( $samples=69$ ). - All images, instructions, solution, and reasoning are manually annotated and validated. - With our instruction design “please select from A, B, C, D, and E." and our LLM answer evaluator, we can assess different reasoning skills and capabilities and easily perform quantitative statistical analysis based on the natural language output of MLLMs. Additionally, We provide more in-depth human-written explanations for why each answer is correct, allowing for thorough open-ended evaluation. As shown in Figure. 1, LogicVista covers a wide range of reasoning capabilities and evaluates them comprehensively. For instance, answering the question “Which of these images is the top view of the given object" in Figure 1 (b) requires not only recognizing the objects’ orientation but also the ability to spatially reason over the object from a different perspective. Since these questions and diagrams are presented without context, they effectively probe the MLLM’s underlying ability rather than relying on contextual cues from the surrounding real-life environment. Furthermore, we provide two evaluation strategies with our annotations: multiple-choice question (MCQ) evaluation and open-ended evaluation. Our annotation of MCQ choices along with our LLM evaluator allows quick evaluations of answers provided by MLLMs. Additionally, our annotation of the reasoning and thought process behind each MCQ enables open-ended evaluation, capturing the nuances of the MLLM responses and identifying which reasoning steps were correct or incorrect. We comprehensively evaluate the performance of 8 representative open and closed source MLLMs on 448 tasks across 5 main logical reasoning categories. LogicVista’s evaluation strategy allows users to see a detailed breakdown of an MLLM’s performance on each reasoning skill and capability. This approach provides more insights than a single overall score, enabling users to better understand the specific skills in which a model excels or needs improvement. 2 Related Works | | VQAv2 [8, 15] | COCO [16] | TextCaps [17] | Contextual [18] | MM-vet [10] | MathVista [14] | VisIT-Bench [19] | LogicVista | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Number of Logical Reasoning Skills Tested | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 5 | | Number of Multimodal Capabilities Tested | 1 | 1 | 2 | 2 | 6 | 12 | 2 | 9 | | Dataset Size | 204,721 | 330,000 | 28,000 | 506 | 217 | 6,141 | 592 | 448 | | Scene and Object Recognition | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | Inductive Reasoning | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✓ | | Deductive Reasoning | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | | Numerical Reasoning | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | Spatial Reasoning | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | | Mechanical Reasoning | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | | Answer Choice Explanations | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✓ | | Human Annotation | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | Human Evaluation | ✗ | ✓ | ✓ | ✓ | ✗ | ✓ | ✓ | ✗ | | Auto/GPT-4 Evaluation | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | Open-ended Evaluation | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Table 1: Comparision with related vision-language benchmarks. Multimodal Language Models The field of vision-language models [20, 21, 22, 23, 24, 25, 26, 27, 28, 29] has made significant progress towards achieving a cohesive understanding and generation of both visual and linguistic information. This progress is largely driven by the remarkable generalization and quality capabilities of recent large language models (LLMs) [30, 1, 31, 32]. As a result, there has been a surge in the development of MLLMs that aim to integrate the diverse capabilities of vision and language for complex multimodal tasks. Efforts to create these multimodal generalist systems include enhancing LLMs with multi-sensory processing abilities, as demonstrated by innovative projects like Frozen [33], Flamingo [2], PaLM-E [34], and GPT-4 [1]. Recent releases of open-source LLMs [35, 32, 36] have further propelled research in this field, leading to the development of OpenFlamingo [37], LLaVA [38], MiniGPT-4 [4], Otter [39], InstructBLIP [40], among others [41, 38, 42]. Additionally, multimodal agents [43, 44, 45] have been explored for their ability to link various vision tools with LLMs [30, 1], aiming to enhance integrated vision-language capabilities Vision-Language Benchmarks Traditional vision-language benchmarks have focused on assessing specific capabilities, including visual recognition [21], generating image descriptions [20, 46], and other specialized functions such as understanding scene text [47, 17, 48], commonsense reasoning [49], mathematical reasoning [14], instruction following [19], and external knowledge incorporation [50]. While some benchmarks incorporate reasoning [18], they are often presented in real-life contexts, which may reduce the task to mere recognition based on contextual cues. The emergence of general MLLMs has highlighted the need for updated vision-language benchmarks that encompass complex multimodal tasks requiring comprehensive vision-language skills. Our benchmark, LogicVista, aligns closely with recent evaluation studies like MM-Vet and MMBench [10, 51], which aim to provide thorough evaluations of MLLMs through well-designed evaluation samples. A key distinction of LogicVista lies in its focus on integrated vision-language capabilities, offering deeper insights beyond mere model rankings. LLM-Based Evaluation. LogicVista adopts an open-ended LLM-based evaluation approach, which facilitates the generation and assessment of diverse answer styles and question types beyond the limitations of binary or multiple-choice responses. This innovative method leverages the capabilities of large language models (LLMs) for comprehensive model evaluation, a technique that has been effectively applied in natural language processing (NLP) tasks [52, 53, 54, 55]. Our findings indicate that this LLM-based evaluation framework is not only versatile but also robust, enabling a unified and flexible assessment across various modalities. By accommodating a wide range of answer styles and question types, this approach enhances evaluation depth and breadth, which contributes to a more thorough understanding of model performance. 3 Data annotation and organization <details> <summary>x1.png Details</summary>  ### Visual Description ## Diagram: Closed-Source Tests System Architecture ### Overview The diagram illustrates a closed-source testing framework with six identical clipboard icons arranged in a 3x2 grid. A central blue lock with radiating lines connects to three distinct elements via arrows: an envelope with an "@" symbol, a stack of coins and dollar bill, and two human figures with a "+" sign. All elements are rendered in black and white except the blue lock. ### Components/Axes 1. **Header**: - Title: "Closed-Source Tests" (top-center, bold black text) 2. **Main Grid**: - Six identical clipboard icons (3 rows × 2 columns) - Each clipboard contains: - Top-right: Checkmark symbol - Bottom-right: Text block (illegible) - Top-left: Text block (illegible) 3. **Central Element**: - Blue lock icon with keyhole - Radiating gray lines (8 total) connecting to three downstream elements 4. **Downstream Elements**: - Left: Envelope with "@" symbol (email) - Center: Stack of coins (3 stacks) + green dollar bill - Right: Two human figures (outline) with "+" superscript ### Detailed Analysis - **Clipboard Grid**: All six clipboards are identical in layout and positioning. No discernible text content due to low resolution. - **Lock Mechanism**: Blue lock centrally positioned below the grid, acting as a security/access control point. Radiating lines suggest bidirectional communication or data flow. - **Arrow Connections**: - Lock → Envelope (left) - Lock → Money (center) - Lock → People (right) - **Symbolic Elements**: - "@" symbol on envelope implies email communication - "$" on bill confirms financial transactions - "+" on people suggests collaboration/team expansion ### Key Observations 1. **Security-Centric Design**: The lock's central position and radiating lines emphasize restricted access to test materials. 2. **Tripartite Output**: The system connects to three distinct domains: communication, finance, and human resources. 3. **Uniform Testing Process**: Identical clipboard icons suggest standardized testing procedures across all six instances. ### Interpretation This diagram represents a closed-source testing ecosystem where: 1. **Test Materials** (clipboards) are secured behind access controls (lock) 2. **Outputs** flow to three critical domains: - **Communication** (email via "@" symbol) - **Financial Tracking** (currency symbols and stacks) - **Team Collaboration** (human figures with "+" indicating growth) 3. The checkmarks on clipboards likely denote completed test cycles, while the illegible text blocks may represent test case details or results. The blue lock's radiating lines suggest the system maintains strict control over test integrity while enabling monitored interactions with external stakeholders (email), financial systems (currency), and team dynamics (collaboration). The absence of numerical data implies this is a conceptual architecture rather than a quantitative analysis. </details> (a) <details> <summary>x2.png Details</summary>  ### Visual Description ## Diagram: Manual Curation Workflow for Annotated Dataset ### Overview The diagram illustrates a multi-step process for curating an annotated dataset, involving human input, data processing, and output generation. It uses visual metaphors (lock icon, document icons) to represent security, documentation, and structured data. ### Components/Axes 1. **Input Elements**: - Three smiling human figures (left side) with dashed arrows pointing to a central box. - Central box labeled with six document icons (representing raw data or initial inputs). - Blue lock icon at the bottom of the central box (symbolizing security/access control). 2. **Output Elements**: - Annotated dataset (right side) containing: - Two image thumbnails (orange/yellow gradient backgrounds). - JSON file icon (bottom right). - Dashed arrows connecting the central box to the annotated dataset and JSON file. 3. **Textual Labels**: - "annotated dataset" (top right). - "JSON" (bottom right). - "Manual Curation of images, answers, and reasoning" (bottom center). ### Detailed Analysis - **Flow Direction**: Left-to-right progression from human input → central processing → structured output. - **Key Relationships**: - Human figures → Central box (manual curation). - Central box → Annotated dataset (data transformation). - Central box → JSON file (structured data export). - **Visual Metaphors**: - Lock icon: Implies secure handling of sensitive data. - Document icons: Represent unstructured/raw data. - Dashed arrows: Suggest iterative or non-linear refinement steps. ### Key Observations 1. The process emphasizes human-in-the-loop curation ("Manual Curation" text). 2. Security is explicitly highlighted via the lock icon, suggesting sensitive data handling. 3. Outputs are dual-format: visual (images) and machine-readable (JSON). 4. No numerical data or quantitative metrics are present in the diagram. ### Interpretation This diagram represents a **data annotation pipeline** where human experts manually curate and validate raw data (images/documents) before producing a structured, annotated dataset and exportable JSON file. The lock icon implies compliance with data privacy standards (e.g., GDPR), while the dual output formats suggest the dataset is intended for both human review and algorithmic use. The absence of quantitative metrics indicates this is a conceptual workflow rather than a performance measurement tool. </details> (b) Figure 2: a) Data collected for LogicVista were gathered from closed sources to avoid data leakage. b) Manual annotators used the gathered tests, gathered the correct answers, and came up with reasonings on why the selected answers were correct. All these annotations were then stored in JSON format. 3.1 Data Sources To ensure the integrity and quality of LogicVista’s evaluations, we have implemented a stringent data collection and curation process specifically designed to prevent data leakage detailed in Figure. 2. Our approach involves sourcing and annotating our samples from proprietary sources that require licenses, registration, payment, or a combination of these barriers to access. This methodology is critical to minimizing the risk that our benchmark data has been previously seen or utilized in the training of other multi-modal models. We prioritized sourcing data from closed sources to further reduce the potential of data leakage. - Licensed Access: We obtain data from sources that require formal licensing, ensuring the data is used solely for research purposes and not freely available for general use or scraping on the internet. - Registration Requirements: Some of our data sources mandate user registration and account verification, adding an additional layer of access control to ensure that the data remain restricted and not easily accessible. - Paid Content: We utilize paid sources where content is accessible only through purchase or subscription, further restricting the data from being freely available on the internet. Additionally, we obtained permission from the creators of IQ tests and other evaluation materials included in our dataset. This permission specifically allows the use of their content for research purposes, ensuring the data’s legitimacy and accuracy. 3.2 Annotation and Data Collection LogicVista consists of images designed to assess the underlying reasoning capacities of MLLMs. Using real-life scenes as explicit tests of logical reasoning can be challenging, as they often contain context clues that AI agent can use to deduce answers without directly reasoning through the scene. Therefore, LogicVista presents multiple-choice questions across 9 explicit capabilities that specify the type of reasoning required, without the additional context of real-life scenes typically found in intelligence and reasoning tests. The dataset is manually collected and annotated from various licensed intelligence test sources. Over a period of 3 months, 5 annotators extracted images, correct answers, and explanations when available. The explanations detailing the reasoning behind answer choices were extensively annotated and cross-validated among annotators, ensuring data integrity through multiple rounds of quality checks. The data is structured in JSON format to facilitate easy retrieval and processing in our evaluation pipeline. For our evaluation, we focused on summarizing five reasoning skills spanning two multimodal capabilities. For detailed examples of these reasoning skills and capabilities, please refer to Appendix. A and Appendix. B. <details> <summary>x3.png Details</summary>  ### Visual Description ## Pie Charts: Reasoning Skills and Capabilities ### Overview The image contains two adjacent pie charts comparing distributions of reasoning skills and capabilities. Both charts use color-coded segments with percentage labels. The left chart focuses on reasoning skills, while the right chart emphasizes capabilities. ### Components/Axes **Left Chart (Reasoning Skills):** - **Segments:** Mechanical (17.0%), Spatial (18.0%), Numerical (21.0%), Deductive (20.0%), Inductive (24.0%) - **Colors:** Blue, Red, Purple, Yellow, Green - **Text:** Percentages displayed inside segments **Right Chart (Capabilities):** - **Segments:** Diagram (26.4%), OCR (18.7%), Puzzles (20.4%), Patterns (8.4%), Graphs (5.4%), Tables (5.6%), Physics (5.5%), Sequences (6.1%), 3D shapes (3.6%) - **Colors:** Green, Yellow, Purple, Red, Blue, Gray, Pink, Orange, Light Blue - **Text:** Percentages displayed inside segments ### Detailed Analysis **Reasoning Skills Distribution:** 1. Inductive reasoning dominates at 24.0% 2. Numerical reasoning follows at 21.0% 3. Deductive reasoning at 20.0% 4. Spatial reasoning at 18.0% 5. Mechanical reasoning at 17.0% **Capabilities Distribution:** 1. Diagram interpretation leads at 26.4% 2. Puzzles at 20.4% 3. OCR at 18.7% 4. Patterns at 8.4% 5. Graphs at 5.4% 6. Tables at 5.6% 7. Physics at 5.5% 8. Sequences at 6.1% 9. 3D shapes at 3.6% ### Key Observations 1. **Dominant Categories:** - Inductive reasoning (24.0%) and Diagram interpretation (26.4%) are the most prominent in their respective charts - Both charts show a "long tail" with multiple smaller segments (<10%) 2. **Distribution Patterns:** - Reasoning skills show a more balanced distribution (range: 17-24%) - Capabilities show greater disparity (range: 3.6-26.4%) 3. **Color Coding:** - Left chart uses warmer colors (red/yellow) for mid-range skills - Right chart uses cooler colors (blue/green) for higher capabilities - 3D shapes (3.6%) uses the smallest segment with orange color ### Interpretation The data suggests a cognitive profile emphasizing analytical skills over mechanical aptitude, with strong inductive and numerical reasoning capabilities. The capabilities chart reveals a focus on abstract pattern recognition (Diagram, Puzzles) over concrete applications (3D shapes). The significant gap between top capabilities (26.4%) and lower ones (3.6%) indicates potential areas for skill development. The near-equal distribution of reasoning skills (within 7% range) contrasts with the capabilities' wider spread, suggesting that while foundational reasoning is balanced, applied capabilities show more specialization. </details> Figure 3: Proportion of reasoning skills and capabilities. On the left is the proportion of questions belonging to each reasoning skill. These proportions add up to $100\%$ as each skill is independent of another. On the right is the proportion of questions belonging to each multi-modal capability. These do not add up to $100\%$ due to the use of mixed capabilities. 3.2.1 Capabilities We distinguish multimodal capabilities from reasoning skills, considering these capabilities fundamental to understanding a multimodal scene and extracting information. Capabilities refer to the modalities through which logical reasoning questions are delivered. To ensure comprehensive coverage in LogicVista, we have defined a diverse array of 9 capabilities for evaluation. This diversity guarantees that LogicVista thoroughly assess various logical situations that an MLLM may encounter in everyday reasoning. Figure 3 demonstrates how LogicVista contains a balanced mix of capabilities, including samples that utilize multiple capabilities to solve a problem. - Diagrams: Simple flow diagrams and logical diagrams (e.g., Markov diagrams). - OCR: Text embedded within an image (e.g., “gas station” in an image of a gas station). - Patterns: Repeated sequences such as a series of diagrams, numbers, shapes, and objects (e.g., identifying patterns in how a box moves through repeated images of boxes). - Graphs: Mathematical graphs with axes (e.g., graphs of $y=2x$ and $y=x^{2}$ ). - Tables: Data tables (e.g., pie charts and T-tables). - 3D Shapes: The ability to understand and differentiate 3D objects from 2D ones (e.g., recognizing a 3D shape in different rotations). - Puzzles: Puzzles with logical implications embedded within the shapes (e.g., chess puzzles). - Sequences: Sequences of related items or objects (e.g., predicting the next item in a sequence). - Physics: Situations involving physics (e.g., diagrams of projectile motion). 3.2.2 Reasoning Skills The reasoning skills of interest for this benchmark are based on common critical thinking and problem-solving skills used by humans in various contexts. For our evaluation, we summarize these into the following five skills. For our evaluation, we summarize these to include the following 5 skills. As seen in Figure 3, LogicVista encompasses a wide range of all these reasoning skills: - Inductive Reasoning: The ability to infer the next entry in a pattern given a set of observations. This involves making generalizations based on specific observations to form an educated guess. It moves from many specific observations to a generalization. For example, observing that John gets a stomach ache when he eats dairy products leads to the inductive conclusion that he is likely lactose intolerant. - Deductive Reasoning: The ability to conclude a specific case from a general principle or pattern. This involves moving from the general to the specific. For example, from the statement “all men are mortal,” one can deduce that “John is mortal” because John is a man. - Numerical Reasoning: The ability to read arithmetic problems in an image and solve the math equations. For example, given the equation “10 + 10 = ?,” the answer would be “20.” - Spatial Reasoning: The ability to understand the spatial relationships between objects and patterns and reason with those relationships. For example, seeing an unfolded box and understanding what the box would look like when folded. - Mechanical Reasoning: The ability to recognize a physical system and solve equations based on that system or answer questions about it. For example, seeing a set of three gears and understanding which gears will turn clockwise and which will turn counterclockwise. 3.3 LLM-based Multiple Choice Answer Extractor <details> <summary>x4.png Details</summary>  ### Visual Description ## Flowchart: Data Annotation and Evaluation Pipeline ### Overview This flowchart illustrates a multi-stage pipeline for processing an annotated dataset through evaluation models. It includes data annotation, raw output generation, multiple-choice question (MCQ) extraction, and performance evaluation via a bar chart. The process emphasizes automated extraction of answers from textual data and their validation through structured evaluation. ### Components/Axes 1. **Annotated Dataset** - Contains multimodal data (images, text, symbols) - Includes examples like: - "The answer is 76 because..." - "Tom would win the race..." - "The pie chart shows..." - "The next element in the sequence is..." 2. **Raw Open-Ended Outputs** - Textual responses generated from the annotated dataset - Example: "The answer is 76 because..." 3. **Extracted MCQ Answers** - Structured options (A-E) derived from raw outputs - Visualized as a vertical list with checkmarks (✓) and crossmarks (✗) 4. **Evaluation Models** - Represented by a bar chart comparing performance metrics - Categories: - "The answer is 76 because..." (70-75%) - "Tom would win the race..." (75-80%) - "The pie chart shows..." (80-85%) ### Detailed Analysis - **Flow Direction**: Annotated dataset → Raw outputs → MCQ extraction → Evaluation models - **Bar Chart Metrics**: - Categories are labeled with textual examples from the dataset - Performance values are approximate (70-85%) with no explicit numerical labels - Bars are color-coded (pink, yellow, green) but lack a legend ### Key Observations 1. The pipeline emphasizes automated answer extraction from unstructured text. 2. Evaluation models focus on textual coherence and factual accuracy. 3. The bar chart lacks a legend, making color assignments ambiguous. 4. All textual examples follow a "The [subject] [verb]..." structure. ### Interpretation This pipeline demonstrates a system for: 1. **Data Annotation**: Combining multimodal inputs (images, text, symbols) into structured datasets. 2. **Answer Extraction**: Using NLP to identify answers from open-ended responses. 3. **Performance Evaluation**: Quantifying model accuracy through textual examples. The absence of a legend in the bar chart introduces uncertainty in interpreting color-coded performance metrics. The consistent structure of textual examples suggests a focus on factual QA tasks, while the evaluation models prioritize both correctness (e.g., "76" as a numerical answer) and contextual reasoning (e.g., "Tom would win the race"). </details> Figure 4: Pipeline of evaluating open-ended LMM outputs using MCQ answer choice extraction. LLMs generate non-deterministic and open-ended responses [56, 57], making direct evaluation challenging. To address this, we use an LLM evaluator to compare these open-ended responses to our annotations as detailed in 4. This evaluator can assess both MCQ answer choices and the MLLM’s reasoning behind those selections, as both elements are included in our annotations. This step is achieved by feeding various contexts such as the question, and the available choices, along with the LLM-generated answers to an extraction LLM (GPT, LLaMA, etc.). Based on the provided rich context, the LLM can generate the selected letter answer choice. The final output is also repeatedly validated and if the validation fails, the extraction repeats with the provided feedback to obtain correct results. 4 Evaluation Setup | Model | Size | Language Model | Vision Model | | --- | --- | --- | --- | | LLaVA-Vicuna-7B | 7B | Vicuna-7B | CLIP ViT-L/14 | | LLaVA-Vicuna-13B | 13B | Vicuna-13B | CLIP ViT-L/336px | | LLaVA-NeXT-Mistral-7B | 7B | Mistral-7B | CLIP ViT-L/14 | | LLaVA-NeXT-Vicuna-7B | 7B | Vicuna-7B | CLIP ViT-L/14 | | LLaVA-NeXT-Vicuna-13B | 13B | Vicuna-13B | CLIP ViT-L/336px | | LLaVA-NeXT-Nous-Hermes-Yi-34B | 34B | Nous Hermes 2-Yi-34B | CLIP ViT-L/336px | | MiniGPT-4-7B | 7B | Vicuna-7B | BLIP-2 Q-Former | | MiniGPT-4-13B | 13B | Vicuna-13B | BLIP-2 Q-Former | | Otter-9B | 9B | MPT-7B | CLIP ViT-L/14 | | GPT-4 Vision | N/A N/A: Not disclosed | N/A | N/A | | BLIP-2 | 2.7B | OPT-2.7B | EVA-ViT-G | | Pix2Struct | 1.3B | ViT | ViT | | InstructBLIP-Vicuna-7B | 7B | Vicuna-7B | BLIP-2 Q-Former | | InstructBLIP-Vicuna-13B | 13B | Vicuna-13B | BLIP-2 Q-Former | | InstructBLIP-FLAN-T5-xl | 3B | FLAN-T5 XL | BLIP-2 Q-Former | | InstructBLIP-FLAN-T5-xxl | 11B | FLAN-T5 XXL | BLIP-2 Q-Former | Table 2: Summary of the MLLMs used for evaluations in this study. To evaluate the performance of MLLMs on LogicVista, we selected a range of representative models detailed in Table. 2. Specifically, we chose8 models for evaluation, including LLaVA [3, 58], MiniGPT4 [4], Otter [39], GPT-4 Vision [1], BLIP-2 [59], and InstructBLIP [40] We also included pix2struct [60] which has been fine-tuned to understand chart and diagram data. Each model generated outputs using the LogicVista dataset. Our LLM-based multiple-choice extractor was then employed to isolate the multiple-choice selections from the MLLMs’ outputs (which often appear as full-sentence responses rather than single letters) and compare them to the ground truth answers. The overall logical reasoning score is calculated as follows: $$ S=\frac{\sum_{n=1}^{N}s_{i}}{N}*100\% \tag{1} $$ Here, $S$ represents the overall score, $s_{i}$ indicate whether a sample $i$ is evaluated as correct or not (regardless of category), and $N$ is the total number of samples. The score for each reasoning skill subcategory is calculated as: $$ S_{LR}=\frac{\sum_{n=1}^{N_{LR}}s_{i}}{N_{LR}}*100\% \tag{2} $$ where $S_{LR}$ represents the score for a specific reasoning skill category, $N_{LR}$ is the total number of samples in that reasoning skill category, and $s_{i}$ indicate whether a sample $i$ from that category was evaluated as correct. Similarly, the score for each multi-modal capability is calculated as: $$ S_{c}=\frac{\sum_{n=1}^{N_{c}}s_{i}}{N_{c}}*100\% \tag{3} $$ where $S_{c}$ represents the score for a specific capability, $N_{c}$ is the total number of samples in that capability, and $s_{i}$ indicates whether a sample $i$ in the capability category is evaluated correctly. 5 LogicVista Benchmarking and Performance Interpretation 5.1 Logical Reasoning Skills We present the performance results of various multimodal LLMs on LogicVista. Table 3 outlines the outcome for these models across five logical reasoning categories. We analyzed models of different architectures and sizes, benchmarking them against a random baseline that assumes an average of five choices per question in the LogicVista dataset. Our findings indicate that many models perform below expectations, often yielding results that are worse than random guessing. This outcome is somewhat anticipated, given that most training data for multimodal LLMs and LLMs are derived from classical computer vision datasets such as COCO, which focus on recognition tasks rather than complex reasoning. Traditional benchmarks typically emphasize recognition tasks, resulting in a lack of emphasis on reasoning tasks during both training and evaluation phases. This is evident from the observation that while many models excel on recognition-based benchmarks like COCO, TextVQA, and MM-vet, they often struggle to outperform a random baseline on logical reasoning tasks. | Model | Inductive | Deductive | Numerical | Spatial | Mechanical | | --- | --- | --- | --- | --- | --- | | LLAVA7B | 29.91% | 29.03% | 26.32% | 25.32% | 36.49% | | LLAVA13B | 18.69% | 31.18% | 20.00% | 27.85% | 24.32% | | otter9B | 31.78% | 24.73% | 18.95% | 18.99% | 21.62% | | GPT4 | 23.36% | 54.84% | 24.21% | 21.52% | 41.89% | | BLIP2 | 17.76% | 23.66% | 23.16% | 24.05% | 18.92% | | LLAVANEXT-7B-mistral | 16.82% | 34.41% | 23.16% | 21.52% | 22.97% | | miniGPTvicuna7B | 10.28% | 9.68% | 7.37% | 3.80% | 27.03% | | miniGPTvicuna13B | 13.08% | 23.66% | 10.53% | 10.13% | 17.57% | | pix2struct | 12.15% | 6.45% | 2.11% | 7.59% | 17.57% | | instructBLIP-vicuna-7B | 4.67% | 21.51% | 24.21% | 2.53% | 22.97% | | instructBLIP-vicuna-13B | 3.74% | 10.75% | 18.95% | 5.06% | 17.57% | | instructBLIP-flan-t5-xl | 23.36% | 22.58% | 22.11% | 7.59% | 33.78% | | instructBLIP-flan-t5-xxl | 17.76% | 30.11% | 24.21% | 20.25% | 22.97% | | LLAVANEXT-7B-vicuna | 26.17% | 21.51% | 25.26% | 27.85% | 29.73% | | LLAVANEXT-13B-vicuna | 22.43% | 22.58% | 26.32% | 26.58% | 25.68% | | LLAVANEXT-34B-NH | 20.56% | 52.69% | 30.53% | 24.05% | 40.54% | Table 3: LogicVista evaluation results for various multimodal LLMs on each logical reasoning skill are presented as $\%$ , with the highest possible accuracy being $100\%$ . The highest-scoring models are highlighted in green and the lower-scoring models are highlighted in yellow. Upon closer examination, we find that models perform best on deductive, numerical, and mechanical reasoning tasks. These types of reasoning are more prevalent in real-life scenarios, which makes models more adept at handling them. For example, deductive reasoning can be applied in predicting a character’s actions based on a scene, while numerical reasoning is crucial in solving arithmetic visual tasks. Mechanical reasoning involves understanding physical principles and interactions. In contrast, induction and spatial reasoning are less frequently encountered in standard training data, potentially explaining the lower performance of models in these areas. These insights underscore the necessity for enhanced training and evaluation methodologies that prioritize reasoning tasks to bolster the logical reasoning capabilities of multimodal LLMs. 5.2 Visual Capabilities In Table 4, we present the results of multimodal LLMs on logical reasoning tasks across diagrammatic and OCR mediums. Generally, we observe that OCR tasks tend to perform better than diagrammatic tasks. This difference stems from the nature of traditional computer vision tasks, which often prioritize recognizing prominent objects (“landmarks”) in a scene, such as distinct cars, planes, people, or balls. Diagrams, in contrast, lack such prominent features and mainly consist of lines and shapes, making it challenging for models to extract intricate relationships between objects. In OCR tasks, once the text is accurately extracted from the image, the remainder of the reasoning task relies on the underlying LLM’s ability to process and interpret the content. This process typically bypasses the complexities of multimodal reasoning, leading to better performance on OCR tasks compared to diagrammatic tasks. These findings highlight the necessity for enhanced evaluation methodologies tailored to diagrammatic reasoning in multimodal LLMs, as current approaches may overlook critical details inherent in these types of tasks. | Model | Diagram | OCR | Patterns | Graphs | Tables | 3D Shapes | Puzzles | Sequences | Physics | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | LLAVA7B | 29.70% | 28.21% | 30.47% | 25.37% | 25.71% | 22.22% | 28.52% | 25.00% | 43.48% | | LLAVA13B | 21.52% | 22.65% | 16.19% | 16.42% | 20.00% | 31.11% | 26.17% | 15.79% | 26.09% | | otter9B | 23.64% | 20.51% | 30.48% | 14.93% | 22.86% | 13.33% | 26.17% | 26.32% | 24.64% | | GPT4 | 26.06% | 39.74% | 20.95% | 20.90% | 22.86% | 31.11% | 31.25% | 28.95% | 47.83% | | BLIP2 | 20.30% | 21.79% | 20.00% | 17.91% | 24.29% | 17.78% | 22.27% | 15.79% | 20.29% | | LLAVANEXT-7B-mistral | 20.30% | 26.92% | 21.90% | 23.88% | 22.86% | 13.33% | 22.27% | 23.68% | 30.43% | | miniGPTvicuna7B | 10.91% | 11.54% | 12.38% | 7.46% | 8.57% | 11.11% | 9.77% | 7.89% | 23.19% | | miniGPTvicuna13B | 12.73% | 17.52% | 12.38% | 10.45% | 11.43% | 11.11% | 14.84% | 6.58% | 20.29% | | pix2struct | 9.39% | 8.55% | 10.48% | 0.00% | 4.29% | 11.11% | 10.55% | 11.84% | 14.49% | | instructBLIP-vicuna-7B | 11.82% | 21.37% | 7.62% | 22.39% | 22.86% | 6.67% | 10.55% | 0.00% | 24.64% | | instructBLIP-vicuna-13B | 10.91% | 13.68% | 5.71% | 19.40% | 15.71% | 11.11% | 6.25% | 2.63% | 18.84% | | instructBLIP-flan-t5-xl | 20.30% | 22.22% | 20.00% | 17.91% | 22.86% | 13.33% | 18.36% | 15.79% | 33.33% | | instructBLIP-flan-t5-xxl | 20.91% | 24.36% | 22.86% | 20.90% | 25.71% | 20.00% | 21.09% | 14.47% | 21.74% | | LLAVANEXT-7B-vicuna | 26.67% | 23.08% | 26.67% | 20.90% | 27.14% | 33.33% | 26.56% | 19.74% | 30.43% | | LLAVANEXT-13B-vicuna | 25.15% | 22.65% | 23.81% | 20.90% | 27.14% | 26.67% | 24.61% | 15.79% | 27.54% | | LLAVANEXT-34B-NH | 27.58% | 39.32% | 25.71% | 28.36% | 32.86% | 26.67% | 30.86% | 21.05% | 46.37% | Table 4: LogicVista evaluation results on various multimodal LLMs across each multi-modal capability. Accuracy results are presented as $\%$ , with a maximum possible accuracy of $100\%$ . Models achieving the highest scores are highlighted green, while lower-scoring models are highlighted yellow. 5.3 Relationship between Model Size and Performance Figure 5 presents a comparative analysis of the model size and the average score achieved across all logical reasoning tasks and capabilities. Each plot includes a shaded region denoting the 95% confidence interval for the regression estimate, visually representing the uncertainty associated with the regression line. Dot sizes in the scatter plot indicate the number of models with identical parameter counts, illustrating the distribution density. This visual evidence strongly suggests a positive correlation between larger model sizes and improved performance in LogicVista. Specifically, as model size increases, performance tends to improve, indicating that larger models may have greater capacity to handle complex patterns and reasoning tasks. 6 Conclusion Reasoning skills are critical for solving complex tasks and serve as the foundation for many challenges that humans expect AI agents to tackle. However, the exploration of reasoning abilities in multimodal LLM agents remains limited, with most benchmarks and training datasets predominantly focused on traditional computer vision tasks like recognition. For multimodal LLMs to excel in critical thinking and complex tasks, they must comprehend the underlying logical relationships inherent in these challenges. <details> <summary>x5.png Details</summary>  ### Visual Description ## Scatter Plot: Model Size vs Average Reasoning and Capability Accuracy ### Overview The image is a scatter plot comparing model size (in billions of parameters) to average accuracy in reasoning and capability tasks. Two data series are plotted: "Capability Avg" (red) and "Reasoning Avg" (blue), each with a trend line and shaded confidence interval. The plot includes axis labels, a legend, and numerical annotations for trend lines. --- ### Components/Axes - **X-axis**: Model Size (Billions) - Scale: 0 to 35 (increments of 5) - Labels: "Model Size (Billions)" - **Y-axis**: Average Accuracy (Percent) - Scale: 0 to 60 (increments of 10) - Labels: "Average Accuracy (Percent)" - **Legend**: - Red: "Capability Avg" - Blue: "Reasoning Avg" - **Trend Lines**: - Red (Capability): `y = 0.48x + 14.91` (R² = 0.65) - Blue (Reasoning): `y = 0.55x + 15.41` (R² = 0.68) - **Shaded Regions**: - Light blue (Reasoning): ±2% around the blue trend line - Light red (Capability): ±2% around the red trend line --- ### Detailed Analysis #### Data Points - **Capability Avg (Red)**: - (0, 9), (3, 20), (6, 21), (9, 22), (12, 18), (15, 17), (35, 31) - **Reasoning Avg (Blue)**: - (0, 9), (3, 22), (6, 22), (9, 23), (12, 22), (15, 19), (35, 33) #### Trend Lines - **Capability Avg**: - Slope: 0.48 (moderate increase) - Intercept: 14.91 - R²: 0.65 (65% variance explained) - **Reasoning Avg**: - Slope: 0.55 (steeper increase) - Intercept: 15.41 - R²: 0.68 (68% variance explained) #### Shaded Regions - Both trend lines have ±2% confidence intervals, widening slightly at higher model sizes. --- ### Key Observations 1. **Positive Correlation**: Both capability and reasoning accuracy increase with model size. 2. **Steeper Growth for Reasoning**: The blue trend line (Reasoning) has a higher slope (0.55 vs. 0.48), indicating faster improvement. 3. **Variability**: Larger models (e.g., 35B) show wider shaded regions, suggesting greater uncertainty in accuracy measurements. 4. **R² Values**: Both trends explain ~65-68% of variance, implying model size is a strong but not sole predictor of accuracy. --- ### Interpretation - **Model Size Impact**: Larger models improve performance in both reasoning and capability tasks, but reasoning accuracy grows more rapidly. - **Confidence Intervals**: The shaded regions highlight that accuracy estimates for larger models are less precise, possibly due to increased complexity or measurement noise. - **Practical Implications**: While model size is critical, other factors (e.g., architecture, training data) may also influence accuracy, as R² values are below 1. - **Anomalies**: The red data point at (15B, 17%) deviates slightly from the trend, suggesting potential outliers or measurement errors. This analysis underscores the trade-off between model size and performance gains, emphasizing the need for balanced optimization in AI development. </details> Figure 5: correlation between model size and average accuracy. The scatter plot uses varying dot sizes to represent the density of models with identical sizes. To address this gap, we introduce LogicVista, a novel benchmark designed to evaluate multimodal LLMs through a comprehensive assessment of logical reasoning capabilities. This benchmark features a dataset of 448 samples covering five distinct reasoning skills, providing a robust platform for evaluating cutting-edge multimodal models. Our evaluation aims to shed light on the current state of logical reasoning in multimodal LLMs. To facilitate straightforward evaluation, we employ an LLM-based multiple-choice question-answer extractor, which helps mitigate the non-deterministic nature often associated with multimodal LLM outputs. While LogicVista primarily focuses on explicit logical reasoning tasks isolated from real-life contexts, this approach represents a crucial step toward understanding fundamental reasoning skills. However, it is equally important to explore how AI agents perform tasks that blend abstract reasoning with real-world scenarios, a direction that will guide our future research endeavors. Acknowledgements We extend our sincere appreciation to the student researchers at the University of California, Los Angeles, for their diligent efforts in the manual annotation and validation of our dataset: Evan Li, Srinath Saikrishnan, Lawrence Li, and Oscar Cooper Stern. 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Appendix: LogicVista: Multimodal LLM Logical Reasoning Benchmark in Visual Contexts Appendix A Examples of LogicVista Logical Reasoning Data Table 5: Three samples requiring inductive logical reasoning skills. | (Case A) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/ind1.png Details</summary>  ### Visual Description ## Diagram: Hexagonal Symbol Arrangement ### Overview The image displays five hexagonal shapes labeled **A, B, C, D, E**, arranged in two rows (top and bottom). Each hexagon contains a **circle** and an **arrow**, positioned in specific corners. No numerical data, axes, or legends are present. ### Components/Axes - **Labels**: A, B, C, D, E (textual identifiers). - **Symbols**: - **Circle**: Appears in one corner of each hexagon. - **Arrow**: Appears in another corner of each hexagon. - **Positioning**: - **Top Row**: A (circle top-left, arrow bottom-left), B (circle bottom-left, arrow top-right), C (circle bottom-left, arrow bottom-right), D (circle top-right, arrow bottom-right), E (circle top-right, arrow bottom-left). - **Bottom Row**: A (circle top-left, arrow bottom-left), B (circle bottom-left, arrow top-right), C (circle bottom-left, arrow bottom-right), D (circle top-right, arrow bottom-right), E (circle top-right, arrow bottom-left). ### Detailed Analysis - **Hexagon A**: Circle in top-left corner, arrow in bottom-left corner. - **Hexagon B**: Circle in bottom-left corner, arrow in top-right corner. - **Hexagon C**: Circle in bottom-left corner, arrow in bottom-right corner. - **Hexagon D**: Circle in top-right corner, arrow in bottom-right corner. - **Hexagon E**: Circle in top-right corner, arrow in bottom-left corner. ### Key Observations - No numerical values, scales, or legends are present. - The arrangement of symbols (circle and arrow) varies systematically across the hexagons. - The labels (A–E) are positioned below each hexagon. ### Interpretation The diagram likely represents a **process flow** or **state transitions**, where each hexagon corresponds to a step or condition. The **circle** and **arrow** may symbolize: - **Circle**: A state, node, or reference point. - **Arrow**: Direction of movement, transition, or action. The systematic variation in symbol placement suggests a **logical sequence** or **decision tree**, though no explicit rules or data are provided. The absence of numerical data limits quantitative analysis, but the visual pattern implies a structured relationship between the hexagons. </details> | | | Q: | Which choice (A, B, C, or D) completes the series? | | Answer: | D | | Reasoning: | In this example, there are two rules to be applied. The first is that the circle moves counter-clockwise in the hexagon. It follows that, in the following diagram, the circle will be in the upper corner of the hexagon, pointing to D as the answer. To confirm this, the second rule can be applied, according to which the position of the black triangle alternates between the bottom left and the top right. Thus, in the following diagram, the black triangle will need to be in the upper right corner of the hex. The answer is therefore definitely D. | | Logical Reasoning Skill: | Inductive | | Required capability | Diagram | Table 6: Three samples requiring inductive logical reasoning skills (Case B). | (Case B) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/ind2.png Details</summary>  ### Visual Description ## Grid Rule Analysis: Symbol Pattern Matching ### Overview The image presents two sets of grids. The left set contains two example grids demonstrating a specific symbol arrangement rule. The right set contains four candidate grids (A-D) with the task of identifying which two follow the same rule as the left examples. ### Components/Axes - **Left Grids**: - **Grid 1**: Top row = [Green Square, Purple Circle, Red Cross]; Bottom 3 rows = Blue Triangles - **Grid 2**: Top row = [Purple Circle, Green Square, Red Cross]; Bottom 3 rows = Blue Triangles - **Right Grids (Options)**: - **A**: Top row = [Green Square, Purple Circle, Red Triangle]; Bottom 3 rows = Blue Triangles - **B**: Top row = [Purple Circle, Red Cross, Green Square]; Bottom 3 rows = Blue Triangles - **C**: Top row = [Red Cross, Purple Circle, Green Square]; Bottom 3 rows = Blue Triangles - **D**: Top row = [Red Cross, Purple Circle, Green Square]; Bottom 3 rows = Blue Triangles ### Detailed Analysis 1. **Left Grid Rule Identification**: - **Top Row Pattern**: Contains exactly three symbols: one Green Square, one Purple Circle, and one Red Cross. - **Bottom Rows**: All three rows contain identical Blue Triangles. - **Key Observation**: The top row symbols maintain the same three elements (Square, Circle, Cross) but vary in order. The Cross consistently occupies the third position in both left examples. 2. **Right Grid Evaluation**: - **Grid A**: Replaces Red Cross with Red Triangle in the third position. **Does not match** the required symbol set. - **Grid B**: Contains all three required symbols (Circle, Cross, Square) but rearranged. Cross occupies the second position. **Does not match** the left grids' Cross-in-third-position rule. - **Grid C**: Contains Cross in the first position and Triangle in the second. **Does not match** the required symbol set or Cross position. - **Grid D**: Contains Cross in the first position. **Does not match** the required Cross position. ### Key Observations - **Positional Constraint**: The left grids enforce a strict positional rule where the Red Cross must occupy the third position in the top row. - **Symbol Set Consistency**: All valid grids must contain exactly one instance of each symbol (Square, Circle, Cross) in the top row. - **Bottom Row Uniformity**: All grids share identical Blue Triangles in the bottom three rows, making this a non-discriminating factor. ### Interpretation The rule governing the grids is **twofold**: 1. The top row must contain exactly one Green Square, one Purple Circle, and one Red Cross. 2. The Red Cross must occupy the third position in the top row. **No right grids (A-D) fully satisfy both conditions**. However, if the positional constraint is relaxed (only requiring the presence of all three symbols regardless of order), **Grids B and D** would be the closest matches as they contain the complete symbol set. This suggests either: - A potential error in the question's premise - An implicit rule modification not explicitly stated The strict adherence to Cross position in the left grids implies the rule is position-sensitive, making none of the right grids valid matches under the original constraints. </details> | | | Q: | Two grids containing colored symbols and following a common rule are presented. In the block on the right, four additional grids are presented. The candidate must find the two grids that follow the same rule out of these four options. What options (A, B, C, or D) follow this same rule? | | Answer: | B, D | | Reasoning: | In this example, it is easy to see that the rule governing the two grids on the left is: that blue triangles are present in each of the two bottom lines. This rule is followed in the two grids on the right. | | Logical Reasoning Skill: | Inductive | | Required capability | Diagram, OCR | Table 7: Three samples requiring inductive logical reasoning skills (Case C). | (Case C) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/ind3.png Details</summary>  ### Visual Description ## Chart/Diagram Type: Categorical Symbol Grid ### Overview The image displays a horizontal grid of nine labeled squares (A–I), each containing a geometric shape. The shapes alternate between black diamonds, white diamonds, and one black square (G). The arrangement suggests a categorical comparison or classification system. ### Components/Axes - **Labels**: A, B, C, D, E, F, G, H, I (top of each square). - **Shapes**: - Black diamond (A, C, E, I). - White diamond (B, D, F, H). - Black square (G). - **Legend**: No explicit legend is present, but color/shape differentiation implies a binary (or ternary) classification system. ### Detailed Analysis 1. **Shape Distribution**: - Black diamonds: 4 instances (A, C, E, I). - White diamonds: 4 instances (B, D, F, H). - Black square: 1 instance (G). 2. **Positioning**: - Squares are evenly spaced in a single row. - G (black square) is centrally located (5th position). 3. **Color/Shape Logic**: - Alternating pattern (black/white/diamond) is disrupted by G’s square shape. ### Key Observations - **Symmetry**: The grid exhibits near-symmetry in shape count (4 black diamonds, 4 white diamonds) but asymmetry in shape type (G’s square breaks the diamond pattern). - **Anomaly**: G’s square is the only non-diamond shape, suggesting it represents a distinct category or outlier. - **Labeling**: No additional text or numerical values are present beyond the labels A–I. ### Interpretation The grid likely represents a categorical dataset where: - **Black diamonds** and **white diamonds** denote two primary categories (e.g., "Active" vs. "Inactive" states). - **G’s black square** introduces a third category or an exception, possibly indicating an error, special case, or transitional state. - The absence of a legend leaves the exact meaning of shapes open to interpretation, but the stark contrast between diamonds and the square emphasizes its significance. The structured yet irregular pattern suggests a system designed to highlight deviations or prioritize specific elements (e.g., G as a focal point). Further context would clarify the symbolic meaning of shapes and colors. </details> | | | Q: | Who is the odd-one-out? Select answers from A-I. | | Answer: | G | | Reasoning: | Element G constitutes the exception and is therefore the correct answer. | | Logical Reasoning Skill: | Inductive | | Required capability | Diagram | Table 8: Three samples requiring deductive logical reasoning skills (Case A). | (Case A) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/ded1.png Details</summary>  ### Visual Description ## Logical Deduction Problem: Footballers and Fitness ### Overview The image presents a logical deduction exercise with two premises and five potential conclusions. The task is to identify which conclusion logically follows from the given premises. ### Content Details **Premises:** 1. "All footballers are fit and healthy." 2. "All famous sports players are footballers." **Question:** "Given that the above is true, which of the following is the logical deduction?" **Options:** 1. All footballers are famous sports people 2. All famous people are fit and healthy 3. All famous sports players are fit and healthy 4. All fit and healthy people are footballers 5. All football players are men ### Key Observations - **Premise 1** establishes a universal relationship: Footballers ⊆ Fit and Healthy People. - **Premise 2** establishes another universal relationship: Famous Sports Players ⊆ Footballers. - **Option 3** directly combines the two premises via syllogism: Famous Sports Players ⊆ Footballers ⊆ Fit and Healthy People → Famous Sports Players ⊆ Fit and Healthy People. - **Options 1, 2, 4, and 5** are invalid: - Option 1 reverses the subset relationship (Footballers ⊆ Famous Sports People ≠ Footballers ⊆ Famous Sports People). - Option 2 introduces "famous people" (not limited to sports), which is not supported by the premises. - Option 4 incorrectly generalizes "fit and healthy people" as a subset of footballers. - Option 5 introduces "men," a category not mentioned in the premises. ### Interpretation The problem tests syllogistic reasoning. The correct deduction (Option 3) follows from transitivity: If all famous sports players are footballers, and all footballers are fit and healthy, then all famous sports players must be fit and healthy. The other options either misapply subset relationships, introduce unsupported categories, or reverse logical flow. This exercise highlights the importance of strict adherence to premise boundaries in deductive reasoning. </details> | | | Q: | Which is the correct answer according to the image? Select from 1-5? | | Answer: | 3 | | Reasoning: | Using deductive reasoning, the only logical answer is 3. To get to this answer, you need to simplify the given facts. All famous sports players are footballers, and all footballers are fit and healthy. We can not deduce that all footballers are famous sports people, as we have not got that information. We can not deduce that all famous people are fit and healthy, because the fact is about famous sports people. This is the logical answer. This information is not given; all footballers are fit and healthy but we can not logically link that all fit and healthy people are footballers. This is obviously incorrect, as gender is not mentioned at all in the question. | | Logical Reasoning Skill: | Deductive | | Required capability: | OCR | Table 9: Three samples requiring deductive logical reasoning skills (Case B). | (Case B) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/ded2.png Details</summary>  ### Visual Description ## Textual Content: Multiple-Choice Question on Swallow Colors ### Overview The image contains a multiple-choice question presented in plain text. The question and answer options are formatted with labels (A, B, C, D) and punctuation. No visual elements (e.g., charts, diagrams) are present. ### Components/Axes - **Question**: "The vast majority of swallows are blue. What is the most logical conclusion?" - **Answer Options**: - **A**: "There is a white swallow." - **B**: "Not everything that is blue is a swallow." - **C**: "There is a blue swallow." - **D**: "None of the answers are satisfactory." ### Content Details - **Question Text**: - "The vast majority of swallows are blue." (Premise) - "What is the most logical conclusion?" (Query) - **Answer Text**: - **A**: Asserts the existence of a white swallow. - **B**: States a logical negation ("Not all blue things are swallows"). - **C**: Asserts the existence of a blue swallow. - **D**: Rejects all options as unsatisfactory. ### Key Observations 1. The question tests logical inference from a statistical premise ("vast majority"). 2. Option **C** directly follows from the premise (if most swallows are blue, at least one must be blue). 3. Option **B** introduces a separate logical principle (inverse of the premise). 4. Option **A** is unrelated to the premise (no information about white swallows is provided). 5. Option **D** is a meta-commentary on the validity of the options. ### Interpretation - **Logical Structure**: The premise establishes a probabilistic claim ("vast majority"), which implies the existence of at least one blue swallow. This makes **C** the most direct conclusion. - **Distractors**: - **A** is a non sequitur (irrelevant to the premise). - **B** misapplies logical negation (the premise does not claim *all* blue things are swallows). - **D** is self-referential but does not address the premise’s validity. - **Ambiguity**: The term "vast majority" is vague (e.g., 51% vs. 99%), but even a small majority necessitates at least one blue swallow. This question evaluates understanding of existential quantification and logical fallacies. The correct answer hinges on recognizing that a majority implies existence, not universality. </details> | | | Q: | What is the correct answer to the question in the image? Select from A-D. | | Answer: | C | | Reasoning: | The vast majority of swallows are blue so the answer must be C: there is a blue swallow. | | Logical Reasoning Skill: | Deductive | | Required capability: | OCR | Table 10: Three samples requiring deductive logical reasoning skills (Case C). | (Case C) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/ded3.png Details</summary>  ### Visual Description ## Text Block: Philosophical Statements on Production, Government, and Free-Market Dynamics ### Overview The image contains a block of six declarative statements presented in black text on a white background, framed by a thin yellow border. The content explores the interdependence of societal actors (people, government, free-market) and their roles in determining production and governance. ### Components/Axes - **Textual Content**: Six discrete statements organized vertically. - **Visual Structure**: - Yellow rectangular border (top and bottom edges only). - Uniform black font (Arial-like, 12pt). - No graphical elements, charts, or diagrams. ### Detailed Analysis 1. **"The people determine what is produced."** - Positions individuals as the primary drivers of production decisions. 2. **"The government is made up of the people."** - Establishes government as a collective representation of the populace. 3. **"Production is determined by the free-market."** - Attributes production outcomes to market mechanisms rather than direct human intervention. 4. **"The free-market is made up of production."** - Reciprocal relationship: the free-market is defined by its production activities. 5. **"Government is determined by the free-market."** - Suggests market forces influence governance structures or policies. 6. **Implicit Cyclical Logic**: - The statements form a closed loop: People → Government → Free-Market → Production → Free-Market → Government. ### Key Observations - **Repetition of "free-market"**: Appears in four of six statements, emphasizing its centrality. - **Circular Dependency**: The final statement ("Government is determined by the free-market") closes the loop, implying market forces override democratic governance. - **Contradiction**: While statement 2 claims government is "made up of the people," statement 5 suggests the free-market (not people) determines government, creating tension between direct democracy and market influence. ### Interpretation The text presents a theoretical framework where: 1. **Production** is both a product of the free-market (statement 3) and its defining characteristic (statement 4). 2. **Governance** is paradoxically both a reflection of the people (statement 2) and subordinate to market forces (statement 5). 3. **Agency** shifts from individuals (statement 1) to abstract systems (free-market), suggesting a critique of capitalism's dominance over democratic processes. This structure mirrors classical liberal economic theory, where the free-market is idealized as a self-regulating entity that indirectly shapes societal outcomes, including governance. The cyclical logic implies a deterministic view where human agency is mediated through market mechanisms, raising questions about the balance between popular sovereignty and economic determinism. </details> | | | Q: | What is produced is determined by the people. Select from A, B, and C. (A) True (B)False (C)Insufficient Information? | | Answer: | A | | Reasoning: | Line 1 states that the people determine what is produced. Line 2 states that the government is made up of the people. Therefore, the people determine what is produced. This is a syllogism. Thus, this statement is true. | | Logical Reasoning Skill: | Deductive | | Required capability: | OCR | Table 11: Three samples requiring numerical logical reasoning skills (Case A). | (Case A) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/num1.png Details</summary>  ### Visual Description ## Share Price Index and Dividend Index Tables ### Overview The image presents two comparative tables: 1. **Share Price Index**: Tracks stock prices, daily changes, and 12-month price ranges for five companies. 2. **Dividend Index**: Details interim and final dividends paid per share for the same companies. ### Components/Axes #### Share Price Index Table - **Columns**: - **Company**: Huver Co., Drebs Ltd, Fevs Plc, Fauvers, Steapars. - **Today’s Price (€)**: Current stock price. - **Change from previous day (%)**: Daily percentage change (red for negative values). - **Past 12 months**: - **Max price (€)**: Highest price in the last year. - **Min price (€)**: Lowest price in the last year. #### Dividend Index Table - **Columns**: - **Dividend paid per share (€)**: Dividend amounts. - **Companies**: Huver Co., Drebs Ltd, Fevs Plc, Fauvers, Steapars. - **Rows**: - **Interim Dividend**: Partial dividend payments. - **Final Dividend**: Final dividend payments. - **Note**: Total annual dividend = Interim + Final Dividend. ### Detailed Analysis #### Share Price Index | Company | Today’s Price (€) | Change (%) | Max Price (€) | Min Price (€) | |-------------|-------------------|------------|---------------|---------------| | Huver Co. | 1,150 | +1.10 | 1,360 | 860 | | Drebs Ltd | 18 | +0.50 | 22 | 11 | | Fevs Plc | 1,586 | **-9.00** | 1,955 | 1,242 | | Fauvers | 507 | **-1.00** | 724 | 464 | | Steapars | 2,537 | +1.00 | 2,630 | 2,216 | #### Dividend Index | Dividend Type | Huver Co. (€) | Drebs Ltd (€) | Fevs Plc (€) | Fauvers (€) | Steapars (€) | |---------------------|---------------|---------------|--------------|-------------|--------------| | Interim Dividend | 0.83 | 0.44 | 0.34 | 0.09 | 0.48 | | Final Dividend | 1.75 | 1.12 | 1.25 | 0.32 | 0.96 | ### Key Observations 1. **Share Price Volatility**: - **Fevs Plc** experienced the largest single-day drop (-9.00%), while **Houver Co.** and **Steapars** showed gains (+1.10% and +1.00%, respectively). - **Steapars** has the highest stock price (€2,537) and the widest 12-month range (€2,630–€2,216). - **Fauvers** and **Fevs Plc** are the only companies with negative daily changes. 2. **Dividend Payouts**: - **Houver Co.** offers the highest total annual dividend (€2.58 = 0.83 + 1.75). - **Fauvers** has the lowest interim dividend (€0.09) and **Fevs Plc** the lowest final dividend (€1.25). - **Drebs Ltd** and **Steapars** show balanced dividend distributions. ### Interpretation - **Market Performance**: The negative changes for **Fevs Plc** and **Fauvers** suggest potential financial or sector-specific challenges. In contrast, **Houver Co.** and **Steapars** demonstrate stability or growth. - **Dividend Strategy**: **Houver Co.** prioritizes shareholder returns with the highest dividends, while **Fauvers** and **Fevs Plc** allocate fewer resources to dividends, possibly reinvesting in growth. - **Risk-Return Tradeoff**: **Steapars** combines high stock prices with moderate dividends, indicating a growth-oriented strategy. **Drebs Ltd** balances modest price fluctuations with consistent dividends. ### Spatial Grounding - **Share Price Index**: Top section, dark header row, alternating light/dark rows for companies. - **Dividend Index**: Bottom section, dark header row, light rows for dividend types. - **Color Coding**: Negative price changes (Fevs Plc, Fauvers) highlighted in red. ### Trend Verification - **Share Prices**: - **Fevs Plc**: Sharp decline (-9.00%) despite a 12-month high of €1,955. - **Houver Co.**: Steady growth from €860 (min) to €1,360 (max). - **Dividends**: - **Houver Co.**: Highest interim (€0.83) and final (€1.75) dividends. - **Fauvers**: Minimal interim (€0.09) and final (€0.32) dividends. ### Conclusion The data highlights divergent financial strategies: **Houver Co.** and **Steapars** focus on stability and shareholder returns, while **Fevs Plc** and **Fauvers** face short-term volatility and lower dividend payouts. Investors may prioritize **Houver Co.** for dividends and **Steapars** for growth potential. </details> | | | Q: | Which share had the largest difference between the highest and lowest price over the last 12 months? Select from A, B, C, D and E. (A) Huver Co. (B) Drebs Ltd (C) Fevs Plc (D) Fauvers (E) Steapars | | Answer: | C | | Reasoning: | Step 1- Calculate the difference between the maximum and the minimum prices. Huver Co. = 1,360 - 860 = 500 Drebs Ltd = 22 - 11 = 11 Fevs Plc = 1,955 - 1,242 = 713 Fauvers = 724 - 464 = 260 Steapars = 2,630 - 2,216 = 414. Tip: Notice the wording of the question is asking for the share with the largest absolute change in price, NOT the largest percentage change, which would have been Drebs Ltd. If the question had wanted the percentage change it would have used the word percentage. Thus the correct answer is (C) Fevs Plc | | Logical Reasoning Skill: | Numerical | | Required capability: | OCR | Table 12: Three samples requiring numerical logical reasoning skills (Case B). | (Case B) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/num2.png Details</summary>  ### Visual Description ## Stacked Bar Chart: Reyes Heslop Consulting Profits (£ millions) ### Overview The chart displays segmented bar graphs representing consulting profits (in £ millions) across five sectors (Leisure, Manufacturing, Retail, Government, Utilities) for three regions: Pacific Rim (green), American (blue), and European (dark blue). Each bar is divided into three color-coded segments corresponding to regional contributions. ### Components/Axes - **X-axis**: Sectors (Leisure, Manufacturing, Retail, Government, Utilities) - **Y-axis**: Profit values in £ millions (no explicit scale, inferred from segment heights) - **Legend**: - Green = Pacific Rim - Blue = American - Dark Blue = European - **Segmentation**: Bars are stacked vertically, with European (dark blue) at the base, American (blue) in the middle, and Pacific Rim (green) at the top. ### Detailed Analysis #### Leisure - European: 5.2 (dark blue) - American: 7.4 (blue) - Pacific Rim: 4.6 (green) - **Total**: £17.2M #### Manufacturing - European: 5.0 (dark blue) - American: 7.2 (blue) - Pacific Rim: 6.3 (green) - **Total**: £18.5M #### Retail - European: 4.4 (dark blue) - American: 5.8 (blue) - Pacific Rim: 3.8 (green) - **Total**: £14.0M #### Government - European: 4.5 (dark blue) - American: 5.9 (blue) - Pacific Rim: 3.6 (green) - **Total**: £14.0M #### Utilities - European: 3.5 (dark blue) - American: 5.1 (blue) - Pacific Rim: 6.2 (green) - **Total**: £14.8M ### Key Observations 1. **American Region Dominance**: Consistently the highest contributor across all sectors, peaking in Leisure (£7.4M) and Manufacturing (£7.2M). 2. **Pacific Rim Peaks**: Highest profits in Manufacturing (£6.3M) and Utilities (£6.2M), suggesting stronger performance in industrial/utility sectors. 3. **European Weakness**: Lowest profits in Utilities (£3.5M) and Retail (£4.4M), indicating potential market challenges. 4. **Government Sector**: Uniformly the least profitable across all regions (£3.6M–£4.5M). 5. **Leisure Sector**: Highest total profits (£17.2M), driven by American contributions. ### Interpretation The data reveals regional disparities in consulting demand and profitability. The American region’s dominance in Leisure and Manufacturing aligns with potential economic strength in these sectors. The Pacific Rim’s outperformance in Manufacturing and Utilities may reflect regional industrial growth or strategic focus. European underperformance in Utilities and Retail could signal market saturation or competitive pressures. The Government sector’s consistent low profits across regions might indicate regulatory constraints or lower private-sector engagement. Overall, the chart underscores the importance of sector-specific strategies for regional optimization. </details> | | | Q: | Reyes Heslop had a target for Leisure profits to be a quarter of their total profits. Assuming profits in other areas remain the same, by how much did the Leisure profits miss this target? Select from A, B, C, D and E. (A) 31.8 million (B) 32.4 million (C) 32.7 million (D) 33.2 million (E) 33.4 million | | Answer: | D | | Reasoning: | Step 1- Calculate the total Reyes Heslop profits across all areas other than Leisure. (6.3 + 7.2 + 5.0) + (3.8 + 5.8 + 4.4) + (3.6 + 5.9 + 4.5) + (6.2 + 5.1 + 3.5) = 61.3 million. Step 2- This needs to be 1/4 of all profits for the condition to be met. Therefore all profits, across all sectors, would be 61.3 / 75% = 81.7333 million. Step 3- Now we look at the difference between actual and target Leisure profits. Actual = (4.6 + 7.4 + 5.2) = 17.2 Target = (81.7333 - 61.3) = 20.4333 Shortfall = 3.2333 (millions) Thus the correct answer is (D) 33.2 million | | Logical Reasoning Skill: | Numerical | | Required capability: | Diagram, OCR | Table 13: Three samples requiring numerical logical reasoning skills (Case C). | (Case C) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/num3.png Details</summary>  ### Visual Description ## Pie Charts: Building Energy Use Comparison (1990 vs. 2000) ### Overview Two pie charts compare energy consumption across building spaces in 1990 and 2000. The 1990 chart shows a total of 17,000 kWh, while the 2000 chart totals 15,000 kWh. Both charts categorize energy use into five segments: Meeting Rooms, Kitchen, PC Room, Print Room, and Office Space. ### Components/Axes #### 1990 Chart - **Total Energy Use**: 17,000 kWh - **Segments**: - Meeting Rooms: 12% (dark blue) - Kitchen: 12% (dark blue) - PC Room: 20% (medium blue) - Print Room: 15% (light blue) - Office Space: 41% (lightest blue) #### 2000 Chart - **Total Energy Use**: 15,000 kWh - **Segments**: - Meeting Rooms: 14% (dark blue) - Kitchen: 14% (dark blue) - PC Room: 21% (medium blue) - Print Room: 12% (light blue) - Office Space: 39% (lightest blue) ### Detailed Analysis #### 1990 Data - **Meeting Rooms**: 12% of 17,000 kWh = **2,040 kWh** - **Kitchen**: 12% of 17,000 kWh = **2,040 kWh** - **PC Room**: 20% of 17,000 kWh = **3,400 kWh** - **Print Room**: 15% of 17,000 kWh = **2,550 kWh** - **Office Space**: 41% of 17,000 kWh = **6,970 kWh** #### 2000 Data - **Meeting Rooms**: 14% of 15,000 kWh = **2,100 kWh** - **Kitchen**: 14% of 15,000 kWh = **2,100 kWh** - **PC Room**: 21% of 15,000 kWh = **3,150 kWh** - **Print Room**: 12% of 15,000 kWh = **1,800 kWh** - **Office Space**: 39% of 15,000 kWh = **5,850 kWh** ### Key Observations 1. **Office Space Dominance**: Office Space consumed the largest share in both years (41% in 1990, 39% in 2000), though its share decreased slightly. 2. **Meeting Rooms Growth**: Meeting Rooms increased from 12% to 14%, reflecting a 3.1% rise in energy use despite a 12% drop in total energy. 3. **Print Room Decline**: Print Room energy use dropped from 15% to 12%, a 20% reduction in its share. 4. **PC Room Stability**: PC Room energy use remained relatively stable (20% to 21%), despite a 12% total energy reduction. 5. **Total Energy Reduction**: Total energy use fell by 11.8% (17,000 kWh to 15,000 kWh), suggesting improved efficiency. ### Interpretation The data indicates a shift in energy consumption patterns over the decade. While Office Space remained the largest consumer, its relative share decreased, possibly due to energy-efficient technologies or reduced occupancy. Meeting Rooms and PC Rooms saw proportional increases, suggesting greater reliance on collaborative spaces and computing infrastructure. The 11.8% total energy reduction aligns with broader trends in building efficiency, though the reasons for Print Room’s decline (e.g., digitalization) are not explicitly stated. The consistent growth in Meeting Rooms and PC Rooms highlights evolving workplace dynamics. ### Footer Note The charts include a watermark for "AssessmentDay Practice Test Experts," indicating the source of the data visualization. </details> | | | Q: | Which space experienced the smallest reduction in kWh used between 1990 and 2000? Select from A, B, C, and D. (A) Office Space (B) Print Room (C) Meeting Rooms (D) PC Room | | Answer: | D | | Reasoning: | Step 1- Calculate the value of kWh for 1990 and 2000 for each of the rooms. Room 1990 per kWh 2000 per kWh Meeting Rooms 2.04 2.10 Office Space 6.97 5.85 Print Room 2.55 1.80 PC Room 3.40 3.15 Kitchen 2.04 2.10 Step 2- Subtract the kWh for 2000 from that of 1990 for each of the rooms. Room change (1990 - 2000) kWh Meeting Rooms -0.06 Office Space 1.12 Print Room 0.75 PC Room 0.25 Kitchen -0.06 Step 3- Look for the smallest positive value. Negative values represent an increase between 1990 and 2000. Tip- You only need to perform 4 calculations, as two of the rooms have the same values. Thus, the correct answer is (D) PC Room. | | Logical Reasoning Skill: | Deductive | | Required capability: | Diagram, OCR | Table 14: Three samples requiring spatial logical reasoning skills (Case A). | (Case A) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/spat1.png Details</summary>  ### Visual Description ## Diagram: T-Shape with Square Attachment and Configurations ### Overview The image depicts a 3D spatial diagram featuring a primary structure labeled as a "T-shape with a square attachment" at the top, followed by four distinct configurations (A, B, C, D) below. Each configuration represents a variation in the placement of a small square relative to the main T-shape structure. ### Components/Axes - **Primary Structure**: - A vertical rectangular prism (dark blue) attached to the left side of a horizontal rectangular prism (light blue), forming a T-shape. - A smaller square (dark blue) is positioned at the top-left corner of the vertical prism. - **Configurations (A-D)**: - **A**: Square attached to the left side of the horizontal prism. - **B**: Square attached to the right side of the horizontal prism. - **C**: Square attached to the bottom of the vertical prism. - **D**: Square attached to the top-left corner of the horizontal prism. ### Detailed Analysis - **Primary Structure**: - The T-shape consists of two orthogonal rectangular prisms: one vertical (height > width) and one horizontal (width > height). - The square attachment is consistently dark blue, matching the vertical prism's color. - **Configurations**: - **A**: Square is offset to the left of the horizontal prism, creating an asymmetrical extension. - **B**: Square is offset to the right of the horizontal prism, mirroring the asymmetry of A but in the opposite direction. - **C**: Square is positioned at the base of the vertical prism, extending downward. - **D**: Square is placed at the top-left corner of the horizontal prism, overlapping slightly with the vertical prism. ### Key Observations 1. **Spatial Relationships**: - The square's position varies across configurations, altering the overall geometry of the T-shape. - Configurations A and B are horizontally mirrored, while C and D occupy unique vertical/horizontal positions. 2. **Color Consistency**: - All squares are dark blue, matching the vertical prism's color, suggesting a shared material or functional property. 3. **Symmetry**: - No configuration exhibits perfect symmetry; all introduce asymmetry through square placement. ### Interpretation The diagram likely illustrates a spatial reasoning problem, such as determining the correct assembly of components based on positional constraints. The primary structure serves as a reference, while the configurations (A-D) test understanding of spatial relationships. For example: - **A vs. B**: Tests recognition of left/right orientation. - **C vs. D**: Tests vertical vs. horizontal placement logic. - **D**: Combines horizontal and vertical alignment, requiring multi-axis reasoning. The absence of numerical data or explicit rules implies the focus is on geometric intuition rather than quantitative analysis. This type of diagram is common in puzzles, engineering blueprints, or cognitive tests evaluating spatial awareness. </details> | | | Q: | Which figure is a rotation of the object? Select from A, B, C, and D. (A) (B) (C) (D) | | Answer: | B | | Reasoning: | The answer is B. | | Logical Reasoning Skill: | Spatial | | Required capability: | Diagram | Table 15: Three samples requiring spatial logical reasoning skills (Case B). | (Case B) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/spat2.png Details</summary>  ### Visual Description ## Diagram: Geometric Relationship Illustration ### Overview The image presents a geometric diagram with labeled components and four alternative configurations (A, B, C, D) below. The main diagram includes a rectangle divided into sections with algebraic relationships, while the options depict variations of stepped or angular shapes. ### Components/Axes - **Main Diagram Labels**: - Top-left: "a" (horizontal line) - Bottom-left: "b" (horizontal line) - Center: "2a" (vertical line) and "a" (horizontal line) - Top-right: "b = a + ½a" (equation) - Bottom-right: "2b" (horizontal line) - **Options A-D**: - **A**: Stepped shape with a horizontal top segment, vertical drop, and horizontal base. - **B**: Vertical segment on the left, diagonal slope, and horizontal base. - **C**: Diagonal slope on the left, horizontal segment, and stepped base. - **D**: Diagonal slope on the left, horizontal segment, and stepped base (similar to C but with a different slope angle). ### Detailed Analysis 1. **Main Diagram**: - The rectangle is divided into sections with labeled lengths: - Left side: "a" (height) and "2a" (height). - Bottom: "b" (width) and "2b" (width). - Equation: "b = a + ½a" (top-right corner), indicating a proportional relationship between "a" and "b". - Spatial grounding: Labels are positioned adjacent to their respective lines (e.g., "a" above the left vertical line). 2. **Options A-D**: - All options share a common structure: a diagonal slope on the left, a horizontal segment, and a stepped base. - Differences: - **A**: Horizontal top segment aligns with the main diagram’s "2a" height. - **B**: Vertical segment matches the main diagram’s "a" height. - **C** and **D**: Stepped bases vary in width and slope angle. ### Key Observations - The equation "b = a + ½a" suggests a dependency of "b" on "a", with "b" being 1.5 times "a". - Options A-D likely represent alternative configurations of the main diagram’s components, with variations in slope angles and segment lengths. - No numerical values or units are provided, leaving relationships abstract. ### Interpretation The diagram illustrates a geometric relationship where "b" is derived from "a" via the equation. The options (A-D) may represent practical applications or variations of this relationship, such as different ways to partition or construct shapes based on the proportional rule. The absence of units implies a theoretical or schematic purpose, possibly for educational or design contexts. The stepped configurations in A-D could symbolize iterative adjustments or optimizations of the base relationship. </details> | | | Q: | Which figure can be formed with the given piece? Select from A, B, C, and D. (A) (B) (C) (D) | | Answer: | C | | Reasoning: | The answer is C. | | Logical Reasoning Skill: | Spatial | | Required capability: | Diagram | Table 16: Three samples requiring spatial logical reasoning skills (Case C). | (Case C) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/spat3.png Details</summary>  ### Visual Description ## Diagram: 2D Layout with 3D Structural Options ### Overview The image presents a technical diagram divided into two sections: 1. **Top Section**: A 2D layout of a square divided into geometric regions with a central circular element and connecting lines. 2. **Bottom Section**: Four 3D structural diagrams labeled **A**, **B**, **C**, and **D**, each depicting variations of a cylindrical object integrated into a rectangular framework. ### Components/Axes #### Top Section (2D Layout): - **Square Framework**: A large square divided into three distinct regions: - **Left Region**: A smaller square (occupies ~1/4 of the square’s width). - **Middle Region**: A vertical rectangle (occupies ~1/2 of the square’s width). - **Right Region**: A larger horizontal rectangle (occupies ~1/4 of the square’s width). - **Central Circle**: A circle positioned at the junction of the middle and right regions. - **Connecting Lines**: - A vertical line extends downward from the circle’s center to the bottom edge of the square. - Two diagonal lines extend from the circle’s center to the top and bottom edges of the right region. #### Bottom Section (3D Diagrams): - **Labels**: Four options labeled **A**, **B**, **C**, and **D**. - **Common Elements**: - A **cylindrical object** (vertical or horizontal orientation). - A **rectangular framework** with internal subdivisions. - **Differences**: - **A**: Vertical cylinder with a horizontal rectangular base. - **B**: Horizontal cylinder with a vertical rectangular base. - **C**: Horizontal cylinder with a diagonal rectangular base. - **D**: Vertical cylinder with a diagonal rectangular base. ### Detailed Analysis #### Top Section: - The 2D layout resembles a blueprint or schematic. The central circle likely represents a pivotal component (e.g., a joint, hub, or connection point). - The diagonal lines from the circle to the right region’s edges suggest structural supports or alignment guides. #### Bottom Section: - **A**: Vertical cylinder aligned with the middle region’s axis, suggesting a direct vertical integration. - **B**: Horizontal cylinder spanning the width of the square, implying lateral stability. - **C**: Horizontal cylinder with a diagonal base, indicating a slanted or inclined structural relationship. - **D**: Vertical cylinder with a diagonal base, combining vertical and angular elements. ### Key Observations 1. The 2D layout’s central circle and connecting lines may correspond to the cylindrical object’s placement in the 3D diagrams. 2. Diagrams **A** and **D** share a vertical cylinder, while **B** and **C** use a horizontal cylinder. 3. The diagonal bases in **C** and **D** introduce angular complexity absent in the 2D layout. ### Interpretation The diagram likely illustrates engineering or architectural design options for integrating a cylindrical component into a rectangular framework. The 2D layout serves as a conceptual guide, with the 3D diagrams offering practical implementations: - **A** and **D** prioritize vertical alignment, suitable for load-bearing or axial applications. - **B** and **C** emphasize horizontal distribution, potentially for stability or space optimization. - The diagonal bases in **C** and **D** may address uneven load distribution or terrain constraints. The absence of numerical data or explicit annotations suggests the diagram focuses on spatial relationships and structural logic rather than quantitative analysis. </details> | | | Q: | To which object does the given top view correspond? Select from A, B, C, and D. (A) (B) (C) (D) | | Answer: | A | | Reasoning: | The answer is A. | | Logical Reasoning Skill: | Spatial | | Required capability: | Diagram | Table 17: Three samples requiring mechanical logical reasoning skills (Case A). | (Case A) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/mech1.png Details</summary>  ### Visual Description ## Diagram: Gas Cylinder Release Mechanism ### Overview The image depicts a simplified grayscale diagram of a cylindrical gas cylinder with a valve assembly. Bubbles are illustrated rising from the valve, and three downward-pointing arrows are positioned below the cylinder. No textual labels, legends, or numerical data are present. ### Components/Axes - **Primary Elements**: - **Cylinder**: A horizontal, dark gray cylindrical tank with rounded ends. - **Valve Assembly**: A metallic valve with a lever mechanism attached to the cylinder’s right end. - **Bubbles**: Multiple gray spheres ascending vertically from the valve, suggesting gas release. - **Arrows**: Three identical downward-pointing arrows aligned horizontally below the cylinder. - **Spatial Relationships**: - The valve is positioned at the cylinder’s right terminus. - Bubbles originate directly from the valve and ascend in a dispersed pattern. - Arrows are equidistant and parallel, located beneath the cylinder’s base. ### Detailed Analysis - **Valve and Gas Flow**: The valve’s lever is oriented horizontally, implying an open state. The ascending bubbles indicate gas escaping under pressure. No numerical pressure or flow rate values are provided. - **Arrows**: The three downward arrows lack labels or annotations. Their placement and direction suggest a force or flow direction (e.g., gravitational pull, downward gas movement, or structural support). - **Absence of Textual Data**: No labels, legends, or axis markers are visible. The diagram relies solely on visual symbolism. ### Key Observations 1. **Unidirectional Flow**: Gas release is depicted as a singular upward trajectory from the valve. 2. **Ambiguous Arrows**: The purpose of the downward arrows is unclear without contextual labels. 3. **Simplified Representation**: The diagram omits technical details (e.g., pressure gauges, safety mechanisms). ### Interpretation The diagram likely illustrates a conceptual model of gas release from a pressurized cylinder. The upward bubbles emphasize the physical behavior of gas escaping into a less dense medium (e.g., air). The downward arrows may imply: - **Gravitational Influence**: Gas density causing downward movement post-release (contradicting the bubbles’ ascent). - **Structural Support**: Indicating the cylinder’s anchoring mechanism. - **Flow Direction**: A secondary pathway for gas or liquid (e.g., liquid propellant in a gas cylinder). The lack of textual data limits quantitative analysis. The diagram prioritizes symbolic representation over technical precision, making it suitable for educational or conceptual contexts rather than engineering specifications. </details> | | | Q: | A non-pressurised cylindrical metal tank filled with air is submerged underwater. As the air escapes, the tank gradually moves deeper underwater. Which statement provides the best reason for this motion? Select from A, B, C, D, and E. (A) The bubbles provide a downward thrust on the tank (B) The metal increases in density so it gets heavier (C) The bubbles lower the density of the water which lowers its buoyancy (D) Water replaces the air in the tank which makes it heavier (E) Impossible to tell | | Answer: | D | | Reasoning: | As air escapes the available space is quickly replaced with water, so the tank’s density becomes the same as that of the water and with the added weight and density of the tank itself continues to sink. | | Logical Reasoning Skill: | Mechanical | | Required capability: | Diagram | Table 18: Three samples requiring mechanical logical reasoning skills (Case B). | (Case B) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/mech2.png Details</summary>  ### Visual Description ## Diagram: Airflow Scenarios A and B ### Overview The image depicts two side-by-side diagrams labeled "Scenario A" and "Scenario B," illustrating airflow patterns around an open door in a snowy outdoor environment. Both scenarios show a door with a gray frame, snow-covered ground, and pine trees in the background. Arrows indicate airflow direction relative to the door. ### Components/Axes - **Labels**: - "Scenario A" (bottom-left of left diagram) - "Scenario B" (bottom-right of right diagram) - **Arrows**: - **Scenario A**: Three curved arrows pointing outward from the door (leftward and downward). - **Scenario B**: Three curved arrows pointing inward toward the door (rightward and upward). - **Background Elements**: - Snow-covered ground with falling snowflakes. - Silhouettes of pine trees. - Gray door frame with a visible door handle. ### Detailed Analysis - **Scenario A**: - Arrows originate from the door’s interior and curve outward, suggesting air is being expelled from the door into the snowy environment. - No text or numerical data present. - **Scenario B**: - Arrows originate from the snowy environment and curve inward toward the door, indicating air is being drawn into the door from the outside. - No text or numerical data present. ### Key Observations 1. **Opposing Airflow Directions**: - Scenario A shows outward airflow (exhaust), while Scenario B shows inward airflow (intake). 2. **Arrow Placement**: - Arrows are symmetrically positioned in both scenarios but differ in direction. 3. **Environmental Context**: - Snowfall and pine trees suggest a cold, wintry setting. ### Interpretation This diagram likely represents a comparison of ventilation or pressure dynamics in two scenarios: - **Scenario A** could model a situation where indoor air is being expelled (e.g., due to negative pressure or active ventilation). - **Scenario B** might represent air being drawn into a space (e.g., positive pressure or natural convection). The absence of numerical data or explicit legends limits quantitative analysis, but the directional arrows emphasize the qualitative difference in airflow behavior. The snowy environment may imply temperature gradients influencing airflow, though this is not explicitly stated. </details> | | | Q: | It is a cold winter outside and a well-insulated house has its heater turned on. The front door is opened and cold air rushes in. If the wind speed outside is very low, how would the cold air enter the house? Select from A, B, C, D, and E. (A) Scenario A, the cold air will flow towards the floor (B) Scenario B, the cold air will flow towards the ceiling (C) A combination of A and B (D) The cold air will not enter the house (E) Impossible to tell | | Answer: | A | | Reasoning: | Cold air sinks, whereas hot air rises. The house and the air inside it are warmer than the outside air temperature, so if these two systems (house and outside) were to be suddenly connected (door opening) the cold air would sink and the hot air would sit above the cold air until the heat transferred between the two. | | Logical Reasoning Skill: | Mechanical | | Required capability: | Diagram | Table 19: Three samples requiring mechanical logical reasoning skills (Case C). | (Case C) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/mech3.png Details</summary>  ### Visual Description ## Gear System Diagram: Mechanical Power Transmission ### Overview The image depicts a mechanical gear system with five interconnected gears. The system includes one brown gear, three blue gears of varying sizes, and one dark blue gear. Chains connect the gears, and a green arrow indicates rotational direction. No textual labels or legends are present. ### Components/Axes - **Gears**: - **Brown Gear**: Smallest gear, positioned at the top-left. - **Large Blue Gear**: Central gear, largest in size, located at the top-right. - **Medium Blue Gear**: Positioned between the brown and large blue gears. - **Small Blue Gear**: Located near the large blue gear, smaller than the medium blue gear. - **Bottom Blue Gear**: Largest blue gear, positioned at the bottom-right. - **Chains**: Black lines connecting gears. - **Rotation Indicator**: Green arrow at the bottom-left, showing clockwise rotation of the bottom blue gear. ### Detailed Analysis - **Connections**: - The brown gear is connected via a chain to the large blue gear. - The medium blue gear is connected to both the brown and large blue gears. - The small blue gear is connected to the large blue gear. - The bottom blue gear is connected to the large blue gear. - **Rotation Dynamics**: - The green arrow indicates the bottom blue gear rotates clockwise. - Connected gears will rotate in opposite directions (e.g., if the bottom blue gear turns clockwise, the large blue gear turns counterclockwise). - **Size Relationships**: - The large blue gear is approximately 3x the diameter of the brown gear. - The medium blue gear is ~1.5x the diameter of the small blue gear. ### Key Observations 1. The system forms a closed loop via chain connections, suggesting synchronized motion. 2. The brown gear’s small size implies it may act as a driver for higher-speed, lower-torque output. 3. The large blue gear’s central position suggests it transmits power to multiple subsystems. 4. No explicit numerical data (e.g., gear ratios, torque values) is provided. ### Interpretation This diagram illustrates a basic gear train for mechanical power transmission. The absence of labels implies the focus is on spatial relationships and motion direction. The green arrow’s indication of clockwise rotation for the bottom blue gear allows inference of rotational directions for other gears: - **Bottom Blue Gear (Clockwise)** → **Large Blue Gear (Counterclockwise)** → **Medium/Small Blue Gears (Clockwise)** → **Brown Gear (Counterclockwise)**. The system likely demonstrates trade-offs between speed and torque, with smaller gears (e.g., brown) increasing rotational speed at the expense of force, while larger gears (e.g., large blue) reduce speed but amplify torque. No textual data or numerical values are present in the image. The analysis is based solely on visual spatial relationships and mechanical principles. </details> | | | Q: | In which direction does the orange gear rotate? Select from A, B, and C. (A) Clockwise (B) Counterclockwise (C) No rotation | | Answer: | A | | Reasoning: | The correct answer is clockwise. | | Logical Reasoning Skill: | Mechanical | | Required capability: | Diagram | Appendix B Examples of Different LogicVista Capabilities Data Table 20: Three samples of diagram, OCR, and mixed LogicVista data (Case A). | (Case A) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/diagramex.png Details</summary>  ### Visual Description ## Diagram: Three Circles with Labels A, B, and C ### Overview The image displays three concentric gray circles arranged horizontally from left to right. Each circle is labeled with a bold uppercase letter: **A** (smallest), **B** (medium), and **C** (largest). No additional text, axes, legends, or numerical data are present. ### Components/Axes - **Circles**: - **Circle A**: Smallest diameter, positioned leftmost. - **Circle B**: Medium diameter, centered between A and C. - **Circle C**: Largest diameter, positioned rightmost. - **Labels**: - All labels (**A**, **B**, **C**) are centered within their respective circles. - No legends, axis titles, or numerical markers are visible. ### Detailed Analysis - **Size Progression**: - Circle A: Approximately 1/3 the diameter of Circle C. - Circle B: Approximately 2/3 the diameter of Circle C. - Circle C: Largest, with no explicit scale provided. - **Spacing**: - Circles are evenly spaced horizontally, with consistent gaps between A-B and B-C. - **Color/Style**: - All circles share the same gray fill and black outline. ### Key Observations 1. The sequence A → B → C suggests a deliberate progression (e.g., size, priority, or categorical order). 2. No overlapping or intersecting elements; all components are isolated. 3. Absence of contextual text (e.g., titles, units) limits interpretive scope. ### Interpretation The diagram likely represents a hierarchical or sequential relationship, with increasing size symbolizing growth, importance, or magnitude. The lack of numerical data or explanatory text implies the focus is on visual comparison rather than quantitative analysis. The uniformity in color and style emphasizes the relationship between the labels and their relative sizes. **Note**: No factual or numerical data is present beyond the labels and size progression. The image serves as a minimalist representation of ordered categories. </details> | | | Q: | Which ball is the heaviest? Select from A, B, C, and D. (A) A (B) B (C) C (D) CAN NOT SAY | | Answer: | D | | Reasoning: | The correct answer is D. | | Logical Reasoning Skill: | Mechanical | | Required capability: | Diagram | Table 21: Three samples of diagram, OCR, and mixed LogicVista data (Case B). | (Case B) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/ocrex.png Details</summary>  ### Visual Description ## Text Question: "Which of these objects will not float on water?" ### Overview The image contains a single line of text posing a question about buoyancy. No visual elements, charts, diagrams, or data tables are present. The text is centered on a plain white background. ### Components/Axes - **Text Content**: "Which of these objects will not float on water?" - **Font**: Standard sans-serif (likely Arial or similar). - **Positioning**: Centered horizontally and vertically on the image. - **No axes, legends, or numerical scales are present.** ### Detailed Analysis - The question is incomplete as no list of objects is provided for evaluation. - Grammatical structure: Interrogative sentence with a missing antecedent ("these objects"). - No technical terms or domain-specific vocabulary beyond "float" and "water." ### Key Observations - The absence of listed objects renders the question unanswerable in its current form. - The phrasing implies a comparison between multiple objects, but none are specified. ### Interpretation This text appears to be a fragment of a larger educational or assessment tool (e.g., a quiz or physics problem set). The missing list of objects suggests either: 1. A formatting error in the source material. 2. An intentional omission requiring prior context (e.g., objects listed in a preceding question). 3. A test of the responder's ability to identify incomplete information. The question hinges on principles of buoyancy (density vs. water displacement), but without specific objects, no scientific analysis can be performed. For example, common test cases might include a steel anchor (sinks), a wooden block (floats), or a helium balloon (floats due to low density). The lack of data prevents application of Archimedes' principle or material density comparisons. </details> | | | Q: | Select from A, B, C, and D. (A) banana (B) scissors (C) empty plastic soda bottle (D) wooden pencil | | Answer: | B | | Reasoning: | The correct answer is B because scissors have metal and are most likely to sink. | | Logical Reasoning Skill: | Deductive | | Required capability: | OCR | Table 22: Three samples of diagram, OCR, and mixed LogicVista data (Case C). | (Case C) | | | --- | --- | | <details> <summary>extracted/5714025/figures/Appendix/mixedex.png Details</summary>  ### Visual Description ## Bar Chart: Legal Sector IT Spending (£ millions) ### Overview The image contains a bar chart titled "Legal Sector IT Spending (£ millions)" and a table titled "Two Legal Sector IT Firms Income for Consultancy Services (10,000s)". The chart visualizes spending trends across three IT categories (Hardware, Software, Consulting) over five years, with Year 5 marked as a projection. The table compares income data for two firms: Make Fit Ltd and Pure Gap Plc. ### Components/Axes - **Chart Elements**: - **X-axis**: Years labeled "Year 1" to "Year 5 projection". - **Y-axis**: Spending in £ millions, ranging from 0 to 50. - **Legend**: Located at the top-right, with color-coded categories: - **Orange**: IT Hardware - **Blue**: IT Software - **Gray**: IT Consulting - **Table Elements**: - **Columns**: Years 1–4, with two firms: - **Make Fit Ltd** (left column) - **Pure Gap Plc** (right column) - **Values**: Income in 10,000s (e.g., 290 = £2.9 million). ### Detailed Analysis #### Chart Data (Approximate Values): - **Year 1**: - IT Hardware: ~30 million - IT Software: ~20 million - IT Consulting: ~10 million - **Year 2**: - IT Hardware: ~45 million - IT Software: ~30 million - IT Consulting: ~20 million - **Year 3**: - IT Hardware: ~35 million - IT Software: ~15 million - IT Consulting: ~15 million - **Year 4**: - IT Hardware: ~40 million - IT Software: ~25 million - IT Consulting: ~15 million - **Year 5 (Projection)**: - IT Hardware: ~45 million - IT Software: ~30 million - IT Consulting: ~20 million #### Table Data: | Year | Make Fit Ltd | Pure Gap Plc | |------|--------------|--------------| | Year 1 | 290 | 230 | | Year 2 | 180 | 310 | | Year 3 | 260 | 300 | | Year 4 | 320 | 290 | ### Key Observations 1. **Chart Trends**: - IT Hardware spending dominates, peaking in Year 2 and Year 5 projections. - IT Software spending dips in Year 3 but recovers by Year 4. - IT Consulting remains relatively stable, with a slight increase in Year 5. 2. **Table Trends**: - Make Fit Ltd shows fluctuating income, peaking in Year 4 (320). - Pure Gap Plc has higher income in Year 2 (310) and Year 3 (300) but declines in Year 4 (290). ### Interpretation - **Spending Patterns**: The legal sector’s IT spending growth (especially Hardware) suggests increasing reliance on technology. The Year 5 projection indicates sustained investment. - **Firm Performance**: Pure Gap Plc outperforms Make Fit Ltd in Year 2 and 3, while Make Fit Ltd leads in Year 4. This divergence may reflect differing strategic priorities or market positioning. - **Anomalies**: The sharp drop in IT Software spending in Year 3 (to £15 million) contrasts with its recovery in later years, potentially signaling a temporary shift in priorities or economic factors. - **Correlation**: While not explicitly stated, the table’s income data could correlate with the chart’s spending trends. For example, Pure Gap Plc’s higher income in Year 2 aligns with its elevated IT Hardware spending that year. ### Spatial Grounding - The legend is positioned at the top-right, ensuring clarity for chart interpretation. - The table is placed below the chart, maintaining a logical flow from spending trends to firm-specific outcomes. ### Final Notes The data highlights the legal sector’s growing IT expenditure, with Hardware and Software as key drivers. The table underscores variability in consultancy firm performance, suggesting opportunities for strategic analysis. Year 5 projections imply optimism about continued growth, though uncertainties remain around the accuracy of these estimates. </details> | | | Q: | Which of the following statements is false regarding legal sector spending between Year 4 and projected Year 5? Select from A, B, C, D, and E. (A) IT consulting will increase by 35 million. (B) IT consulting will match that of year 2. (C) IT software will exceed IT consulting. (D) Spending on IT hardware will decline. (E) None of these. | | Answer: | D | | Reasoning: | Step 1- Check in turn whether each statement is true or false: a) The projected spend on IT consulting is projected to increase by 35 million. Option A is true. b) The projected spend on IT consulting is 320 million, which matches year 2. Option B is true. c) The projected spend on IT software is 330 million and for IT consulting it is 320 million. Option C is true. d) There are increases projected for IT hardware, IT software, and consulting, therefore “spending on IT hardware will decline” is not true. The option for D is false. e) We see that option D is false, so E cannot be the correct answer. Thus the correct answer is (D) Spending on IT hardware, software, and consulting is projected to decline. | | Logical Reasoning Skill: | Numerical | | Required capability: | Diagram, OCR |