ISEE Quantitative Comparisons Question 146: Answer and Explanation

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Question: 146

4.

Note: Figures 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: C

Explanation:

The answer is C

To find the area of an irregularly shaped shaded region, find the areas of the two normal shapes and subtract the smaller from the larger. The area of a rectangle is length × width, so the area of the large rectangle is ab. The area of a square is side2, so the area of the small square is c2. Thus the area of the shaded region is ab - c2.

Plug in easy numbers for a, b, and c, such as a = 4, b = 3, and c = 2. To find the area of an irregularly shaped shaded region, find the areas of the two normal shapes and subtract the smaller from the larger. The area of the rectangle is 12, and the area of the square is 4, so the area of the shaded region is 8. If you plug your three values into Column B, you also get 8.

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