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31 Mar 2016, 00:57
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
96% (00:39) correct
4%
(01:06)
wrong
based on 751
sessions
History
Date
Time
Result
Not Attempted Yet
If x + y = 7 and x – y = 3, then x^2 - y^2 =
A. -4
B. 4
C. 10
D. 21
E. 40
A. -4
B. 4
C. 10
D. 21
E. 40
Updated on: 22 Feb 2021, 11:30
Originally posted by BrentGMATPrepNow on 31 Mar 2016, 07:21.
Last edited by BrentGMATPrepNow on 22 Feb 2021, 11:30, edited 2 times in total.
Last edited by BrentGMATPrepNow on 22 Feb 2021, 11:30, edited 2 times in total.
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Bunuel
APPROACH #1: Factor the difference of squares
Key property: \((a^2 - b^2)=(a+b)(a-b)\)
So, \((x^2 - y^2)=(x+y)(x-y)\)
\(=(7)(3)\)
\(=21\)
Answer: D
APPROACH #2: Solve the system of equations
Given:
x + y = 7
x – y = 3
Add the two equations to get: 2x = 10, which means x = 5
If x = 5, we can plug that value into either equation, to conclude that y = 2
If x = 5 and y = 2, then x² - y² = 5² - 2² = 25 - 4 = 21
Answer: D
Cheers,
Brent
General Discussion
31 Mar 2016, 04:19
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Bunuel
Well, x^2-y^2 = (x + y)(x - y)
substituting each of (x + y) and (x - y) with 7 and 3, respectively as per above, then
x^2-y^2 = 7*3 = 21
Answer is D
