Abstract Reasoning with Symbols Flashcards

Observe the sequence of figures. Which of the answer choices correctly completes the sequence? **Sequence:** 1. A large square, oriented normally. Inside, a small shaded circle is in the top-left corner. 2. A large square rotated 45 degrees (a diamond). Inside, the small shaded circle is in the top-right corner. 3. A large square, oriented normally. Inside, the small shaded circle is in the bottom-right corner. 4. A large square rotated 45 degrees (a diamond). Inside, the small shaded circle is in the bottom-left corner.

Answer: A large square with a shaded circle in the top-left corner.

The sequence follows two distinct patterns. First, the large square alternates between its normal orientation (0 degrees) and a 45-degree rotation. The pattern is Square, Diamond, Square, Diamond, so the next figure must be a Square. Second, the small shaded circle moves one corner clockwise in each step (top-left -> top-right -> bottom-right -> bottom-left). The next position in this clockwise cycle is the top-left corner. Therefore, the correct answer is a normal square with a shaded circle in the top-left corner.

A 3x3 matrix of figures is presented with one figure missing. Analyze the rows and columns to determine the figure that completes the matrix. **Matrix:** - Row 1: [Circle] [Vertical Line] [Circle with a Vertical Line through its center] - Row 2: [Square] [Horizontal Line] [Square with a Horizontal Line through its center] - Row 3: [Upward-pointing Triangle] [Small Dot] [?]

Answer: An upward-pointing triangle with a small dot in its center.

The logical rule for this matrix is that the figure in the third column is a superposition of the figures from the first and second columns in the same row. In Row 1, the circle and vertical line are combined. In Row 2, the square and horizontal line are combined. Following this rule, the triangle from the first column and the dot from the second column in Row 3 must be combined to produce the missing figure.

Which of the following figures is the 'odd one out' based on a common logical rule shared by the other four?

Answer: A hexagon with one diagonal drawn connecting two opposite vertices.

The common rule shared by four of the figures is that they are all constructed using exactly six straight lines. The square with diagonals has 4 sides + 2 diagonals = 6 lines. The pentagon with one internal line has 5 sides + 1 line = 6 lines. The two separate triangles have 3 + 3 = 6 lines. The hexagon with one diagonal has 6 sides + 1 diagonal = 7 lines, which breaks the pattern.

An analogy is presented as 'Figure A is to Figure B as Figure C is to...?'. Identify the figure that correctly completes the analogy. - **Figure A:** A large square containing a small, black circle. - **Figure B:** A large square containing a small, white circle. - **Figure C:** A large, upward-pointing triangle containing a small, black square.

Answer: A large, upward-pointing triangle containing a small, white square.

The relationship between Figure A and Figure B is that the outer shape remains the same, while the color of the inner shape inverts (black becomes white). To complete the analogy, the same transformation must be applied to Figure C. The outer shape (the large triangle) must remain the same, and the color of the inner shape (the small square) must invert from black to white.

Observe the sequence of 2x2 grids. Which grid correctly continues the sequence? **Sequence:** 1. Top-left: Circle, Top-right: Square, Bottom-left: Triangle, Bottom-right: Empty. 2. Top-left: Empty, Top-right: Circle, Bottom-left: Square, Bottom-right: Triangle. 3. Top-left: Triangle, Top-right: Empty, Bottom-left: Circle, Bottom-right: Square.

Answer: Top-left: Square, Top-right: Triangle, Bottom-left: Empty, Bottom-right: Circle.

The underlying pattern is a clockwise rotation of all elements by one quadrant with each step. The element in the top-left moves to the top-right, top-right moves to bottom-right, bottom-right moves to bottom-left, and bottom-left moves to top-left. Applying this rule to Frame 3: The Triangle (top-left) moves to top-right. The Empty space (top-right) moves to bottom-right, but the Circle from bottom-left moves there. Let's re-evaluate. The Circle moves TL -> TR -> BL. Next position is BR. The Square moves TR -> BL -> BR. Next position is TL. The Triangle moves BL -> BR -> TL. Next position is TR. The Empty space moves BR -> TL -> TR. Next is BL. So the final state is TL: Square, TR: Triangle, BL: Empty, BR: Circle.

All figures in Group 1 follow a certain rule, and all figures in Group 2 follow a different rule. Which of the answer choices belongs in Group 1? - **Group 1:** A shape made of two overlapping squares; A five-pointed star; A square with both diagonals drawn. - **Group 2:** A simple triangle; A circle; A U-shape.

Answer: The number '8'.

The defining characteristic of the figures in Group 1 is that they all contain at least one point where lines intersect or cross over each other. The figures in Group 2 are all simple shapes whose lines or curves do not intersect. Among the answer choices, only the number '8' is constructed with lines that cross over, fitting the rule for Group 1.