ISEE Mathematics Achievement Question 6: Answer and Explanation

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Question: 6

6. If the length of the base of a parallelogram is decreased by 30% and the height is increased by 20%, what is the percent decrease in the area of the parallelogram?

  • A. 16%
  • B. 20%
  • C. 24%
  • D. 28%

Correct Answer: A

Explanation:

A

Let b represent the original base, and let h represent the original height. As area of a parallelogram is given by bh, the original area is bh. As the base was decreased by 30%, the new base will be 70% of the original, or 0.7b. As the height was increased by 20%, the new height will be 120% of the original, or 1.2h. Thus the new area is (7b)(1.2h) = 0.84bh. Percent change is found by taking the difference, dividing that by the original, and then multiplying the result by 100: = 0.16, and 0.16 × 100 = 16.

As no original values were given, they do not matter, so you can plug in. Assign 10 to the original base and the original height. Thus, the original area was 100. The new base is 7 (reduced by 30% or 3), and the new height is 12 (increased by 20% or 2). Thus the new area is 84. As the new area is 16

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