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# (x-y)^2-(x+y)^2=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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24 Jul 2016, 03:06
1
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:06) correct 21% (01:56) wrong based on 80 sessions

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(x-y)^2-(x+y)^2=?
1) xy=5
2) x+y=6

*An answer will be posted in 2 days.

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24 Jul 2016, 04:06
The above expression after expanding comes to -4xy = x^2 + y^2 - 2xy - x^2 - y^2 - 2xy

So just xy value is needed to solve the question. Hence answer A is correct.
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24 Jul 2016, 04:15
x^2-2xy+y^2-(x^2+2xy+y^2)
=
x^2-2xy+y^2-x^2-2xy-y^2
=
-4xy

xy=5
S1 suff

S2
only x+y is known

A
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Joined: 12 Sep 2015
Posts: 4000

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24 Jul 2016, 07:05
1
Top Contributor
1
MathRevolution wrote:
(x-y)² - (x+y)² = ?

1) xy = 5
2) x + y = 6

Target question: What is the value of (x-y)² - (x+y)² ?
This is an ideal candidate for REPHRASING the target question.
(x-y)² - (x+y)² = [x² - 2xy + y²] - [x² + 2xy + y²]
= -4xy
Great, this is a much easier expression.
REPHRASED target question: What is the value of -4xy ?

Statement 1: xy = 5
Perfect.
If xy = 5, then -4xy = -4(5) = -20
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x + y = 6
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 0 and y = 6, in which case -4xy = -4(0)(6) = 0
Case b: x = 1 and y = 5, in which case -4xy = -4(1)(5) = -20
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

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Brent
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25 Jul 2016, 15:56
To rephrase this more efficiently, notice that you've got a difference of squares. That means that you can reduce it in a particular way, without having to expand the whole thing:

(x - y)^2 - (x + y)^2

((x - y) - (x + y))((x - y) + (x + y))

(-2y)(2x)

-4xy

Also, there's no reason you can't test cases directly. For example:

(Statement 1): xy = 5
Case 1: x = 5, y = 1
(5 - 1)^2 - (5 + 1)^2 = 16-36 = -20
Case 2: x = 2.5, y = 2
(2.5-2)^2 - (2.5+2)^2 = .25 - 20.25 = -20
etc.
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Math Revolution GMAT Instructor
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25 Jul 2016, 19:32
If we modify the original condition and the question, from (x-y)^2-(x+y)^2=? --> -4xy=? Hence, we only have to know the value of xy and the correct answer is A.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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28 Feb 2019, 09:24
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Re: (x-y)^2-(x+y)^2=?   [#permalink] 28 Feb 2019, 09:24
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