Spatial Reasoning Flashcards

A clock face is reflected in a mirror. The reflected clock appears to show 10:10. What is the actual time?

Answer: 1:50

A clock reflection maps time T to 12:00 − T, so 12:00 − 10:10 = 1:50.

An object casts a square shadow from above, a triangular shadow from the side, and a circular shadow from the front. What shape could the object be?

Answer: A cone with a square base

A square-based cone viewed from above is square, from the side is triangular, and from the front (tilted) can appear circular.

In a sequence of figures, each step forms an n×n grid of dots where n matches the figure number. How many dots are in the 7th figure?

Answer: 49

The 7th figure is a 7×7 grid, giving 7 × 7 = 49 dots.

A 3D staircase block ascending left to right (3 steps) is viewed from the right side. What silhouette is seen?

Answer: A solid rectangle

The right side view of an ascending staircase shows a solid rectangle because the steps stack to fill the full height.

A regular hexagon is divided by drawing lines from its center to each of the 6 vertices. How many equilateral triangles are created?

Answer: 6

Drawing lines from the center to all 6 vertices of a regular hexagon creates exactly 6 equilateral triangles.

You are facing North. You turn 135° clockwise, then 90° counter-clockwise. Which direction are you now facing?

Answer: North-East

From North (0°): +135° clockwise = 135° = South-East; then −90° counter-clockwise = 45° = North-East.

A cube has its top face blue, bottom red, front green, back yellow, left white, and right black. If the cube is tilted forward 90° (green face rises to top), which face now faces front?

Answer: Red

Tilting the cube forward 90° brings the red (bottom) face up to the front position.