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Section 3 of 5 · 5 puzzles

Spatial Reasoning practice

Spatial Reasoning asks you to turn shapes in your head. In a mental rotation puzzle, one option is the target figure turned and the others are mirror images. Try the example, then open the solution for a method that works every time.

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What this section measures

Spatial puzzles test whether you can hold a figure in mind accurately enough to turn it and compare it with another. The figures are always chiral, like hands: no amount of turning makes a figure match its mirror image. The guide to spatial reasoning covers both puzzle types in this section.

Try it

Which option is the target turned, not flipped?

Target

  1. A
  2. B
  3. C
  4. D
Show the solution

The answer is C: the target turned a quarter turn clockwise.

  1. Pick a landmark. The dot marks one end of the long arm. Use it.
  2. Walk the figure. In the target, start at the dot and walk along the long arm toward the bend. At the bend, the short foot turns to your left. (You are walking down the page, and the foot points to the right of the page, which is your left.)
  3. Do the same walk in each option. Start at the dot, walk to the bend, and see which way the foot turns.
  4. Compare. In C, the foot turns left, the same as the target. In A, B and D, it turns right. Turning a figure never changes which way it bends from a landmark. Mirroring always does.

You can also imagine turning the target directly: a quarter turn clockwise lays the long arm flat across the top with the dot on the right, and the foot drops down at the left end. That is option C. The walking method is slower the first time and faster after that, and it works for any angle.

What changes on the real test

Rotation puzzles get harder by using figures with more parts and by turning them through larger or less obvious angles. The two odd-one-out puzzles ask a different question: which of six figures breaks a property the others share. For those, ignore size and angle first and test properties one at a time: number of sides, symmetry, crossings and enclosed regions.

Next, try a number series.

2 questions

Questions

What is the difference between a rotation and a mirror image?

A rotation turns a figure in place, like turning a page on a desk. A mirror image flips it, like turning the page over. A left hand rotated is still a left hand; a left hand mirrored becomes a right hand.

What are the odd-one-out puzzles in this section?

Six figures share a property, such as the number of sides, a line of symmetry or the number of enclosed regions, and one does not. You pick the one that breaks the rule.

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25 puzzles · about 12 min

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