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Picture three overlapping groups of four-sided figures: the group of all rectangles, the group of all rhombuses and the group of all squares. Which statement describes how the three groups sit inside one another?

Competition practiceReasoning & Mental Ability
  • AThe squares are exactly those figures that lie in both the rectangle group and the rhombus group.
  • BThe rectangle group lies entirely inside the rhombus group.
  • CThe rectangle group and the rhombus group share no figure at all.
  • DThe rhombus group lies entirely inside the square group.

Step-by-Step Solution

A rectangle has four right angles; a rhombus has four equal sides. A figure with both properties has four equal sides and four right angles, which is precisely a square, and every square has both properties. So the square group is the overlap of the other two. The traps: rectangles are not all rhombuses (a 3 by 8 rectangle is not), the two groups certainly do overlap (every square is in both), and rhombuses are not all squares (a slanted rhombus has no right angle).
Answer: A) The squares are exactly those figures that lie in both the rectangle group and the rhombus group.

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