Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?
A. 28
B. 39
C. 50
D. 61
E. 72
Every test-taker should know the following quadratic identities:
(x+y)² = x² + y² + 2xy
(x-y)² = x² + y² - 2xy
(x+y)(x-y)² = x² - y²
Substituting
x²+y²=28 and
xy=11 into (x+y)² =
x² + y² + 2
xy, we get:
(x+y)² =
28 + 2*
11 = 50.
The correct answer is
C.
An alternate approach is to BALLPARK.
x and y must have a product of
11, while x²+y² =
28.
If x=3 and y=4, then xy=
12 and x²+y² = 3²+4² =
25.
The values in blue are reasonably close to the values in red.
If x=3 and y=4, then (x+y)² = (3+4)² = 49.
Thus, the correct answer must be close to 49.
Only
C is viable.
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