SAT Math Multiple Choice Practice Question 140: Answer and Explanation

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Question: 140

8. If (x + y)2 = 53 and (x - y)2 = 37, then xy =

A. 4
B. 16
C. 45
D. 90
E. It cannot be determined from the information given.

Correct Answer: A

Explanation:

A. This problem is a lot like Question 5 in that you can (and should) solve it without -bothering to figure out what x and y equal. The key is remembering to use the super-useful -formula I discuss in Chapter 14, the one that says (a + b)2 = a2 + 2ab + b2. Applying this -formula to the information you're given in Question 8 tells you that x2 + 2xy + y2 = 53 and x2 - 2xy + y2 = 37. If you subtract the second equation from the first, the x2 and y2 terms cancel themselves out, leaving you with 2xy - (-2xy) = 53 - 37, which becomes 4xy = 16, so xy = 4.

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