Spatial Reasoning and Patterns Flashcards

A 3x3 grid contains figures that follow a pattern, but one figure is missing. Each row and each column must contain exactly one of each shape (circle, square, triangle) and one of each shading (solid, striped, unfilled). Based on the visible figures, which figure should be in the bottom-right cell? Row 1: [Solid Circle], [Striped Square], [Unfilled Triangle] Row 2: [Striped Triangle], [Unfilled Circle], [Solid Square] Row 3: [Unfilled Square], [Solid Triangle], [ ? ]

Answer: A striped circle

To solve this, we must satisfy the rules for both shape and shading. In Row 3, we already have a square and a triangle, so the missing shape must be a circle. In the third column, we have an unfilled figure and a solid figure, so the missing shading must be striped. Combining these deductions, the missing figure is a striped circle.

Observe the sequence of figures. A small arrow within a 3x3 grid starts in the top-left square pointing right (East). In each subsequent step, the arrow moves one square clockwise around the perimeter and rotates 45 degrees clockwise. What is the position and orientation of the arrow in the fifth step of the sequence?

Answer: In the bottom-right square, pointing West.

Let's trace the two patterns: position and rotation. Position: 1. Top-Left -> 2. Top-Middle -> 3. Top-Right -> 4. Middle-Right -> 5. Bottom-Right. Rotation: 1. East (0°) -> 2. South-East (45°) -> 3. South (90°) -> 4. South-West (135°) -> 5. West (180°). Therefore, in the fifth step, the arrow is in the bottom-right square and is pointing West.

Which of the following 2D nets can be folded to form the cube shown? The cube displays three faces meeting at a vertex: a solid black circle, a solid black square, and a face with vertical stripes.

Answer: A net where the circle, square, and striped faces are arranged around a common corner piece, allowing them to be adjacent when folded.

For the three faces to be visible simultaneously, they must be adjacent to each other and meet at a single corner. The only net that allows for this arrangement is one where the three specified faces can be folded up around a common vertex. Options where key faces are opposite each other or are separated by another face in a straight line are incorrect.

Which of the answer choices is the correct mirror image of the given figure across the dashed vertical line? The figure is a capital letter 'R' with a small, solid black dot attached to the top-right tip of the letter.

Answer: A backward (reversed) capital 'R' with the dot attached to its top-left tip.

A mirror image across a vertical line reflects the object horizontally. The main body of the 'R' will be reversed. The dot, which is on the right side of the original figure, will appear on the left side in the reflection, maintaining its relative top position. Therefore, the result is a backward 'R' with the dot on the top-left.

In a data flow diagram, a square represents a 'Server', a circle represents a 'Database', and a diamond represents a 'User Terminal'. A solid line indicates a 'Direct Connection' and a dashed line indicates a 'Wireless Connection'. Which of the following describes a diagram showing a Server connected to a Database by a solid line, and the same Server connected to a User Terminal by a dashed line?

Answer: A Server has a direct connection to a Database and a wireless connection to a User Terminal.

The description requires translating each shape and line type according to the provided key. The Square is the 'Server'. It is connected to the Circle ('Database') by a solid line ('Direct Connection'). It is also connected to the Diamond ('User Terminal') by a dashed line ('Wireless Connection'). This matches the first statement exactly.

The first figure is transformed into the second. Apply the same transformation to the third figure to find the correct result. Figure 1: A large unfilled square overlapping with a smaller solid black circle. Figure 2: Only the portion of the solid black circle that was *outside* the square is shown. Figure 3: A large unfilled triangle overlapping with a smaller striped star.

Answer: Only the portion of the striped star that was *outside* the triangle.

The transformation rule shown between Figure 1 and Figure 2 is a subtraction: the area of the first shape (square) is subtracted from the second shape (circle), leaving only the non-overlapping part of the second shape. Applying this rule to the third figure, we subtract the area of the triangle from the star, which leaves only the part of the striped star that is outside the triangle.