ISEE Word Problems Question 147: Answer and Explanation

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Question: 147

4. If the length of a rectangle is increased by 20% and the width is decreased by 40%, what is the percent decrease in the area of the rectangle?

  • A. 60%
  • B. 30%
  • C. 28%
  • D. 20%

Correct Answer: C

Explanation:

The answer is C

Assign x and y to the lengths of the rectangle. The original rectangle has an area of xy. If you add 20% to the length x, you will have a length of 1.2x. If you reduce the length y by 40%, you will have a length of 0.6y. Thus, the new area will be 0.72xy, meaning the area was reduced by 0.28 or 28%.

Plug in values for the length and width of the rectangle. Because a square is a type of rectangle and 10 is a great number for percent questions, use 10 for the length and width. The original area is 100. The larger side (20% greater than 10) is now 12 and the smaller side (40% reduction from 10) is now 6. Thus, the new area is 72, meaning there was a decrease of 28. As the original area was 100, 28 out of 100 is 28%.

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