ISEE Quantitative Comparisons Question 168: Answer and Explanation

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Question: 168

9. The perimeter of the square is 36. The perimeter of the rectangle is also 36.

Note: Figure not drawn to scale.

  • A. The quantity in Column A is greater.
  • B. The quantity in Column B is greater.
  • C. The two quantities are equal.
  • D. The relationship cannot be determined from the information given.

Correct Answer: A

Explanation:

A

The sides of the square are 9, as all sides are equal. Thus, the area is 81. While the sides of the rectangle are unknown, try some possibilities to see how the different areas compare to 81. If the sides are 17 and 1, the area is 17. If the side are 10 and 8, the area is 80. There is no way to get the area up to 81 as long the rectangle is not a square.

A square of a given perimeter will always have the greatest possible area as compared to any rectangle with the same perimeter.

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