ISEE Word Problems Question 242: Answer and Explanation

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Question: 242

6. If x2 + y2 = 73, and 2xy = 48, what is the value of (x – y)2?

  • A. 5
  • B. 11
  • C. 25
  • D. 121

Correct Answer: C

Explanation:

The answer is C

First, factor (x - y)2 to x2 - 2xy + y2. Notice that two of these terms combine to x2 + y2, so substitute 73 for these terms. Also substitute 48 for 2xy. The final result is 73 - 48 = 25.

Use guess and check to come up with numbers that work. As 2xy = 48, xy = 24. Thus, x and y can be 1 and 24, 2 and 12, 3 and 8, or 4 and 6. If you substitute 3 and 8 into x2 + y2, you get 73. Substitute 3 and 8 in (x - y)2 to arrive at 25.

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