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

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(x+y)^2-(x-y)^2=?  [#permalink]

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New post 23 Feb 2017, 19:25
1
2
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:00) correct 21% (01:50) wrong based on 152 sessions

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

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

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Re: (x+y)^2-(x-y)^2=?  [#permalink]

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New post 23 Feb 2017, 19:42
1
MathRevolution wrote:
\((x+y)^2-(x-y)^2=?\)

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


\((x+y)^2-(x-y)^2\)
\(=x^2+y^2+2xy-x^2-y^2+2xy\)
\(=4xy\)

St I
xy=5 ==> 4*xy = 4*5 = 20 ----------Sufficient

St II
x+y=6, we have no information about x-y ----------Insufficient

Hence Option A is correct
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Re: (x+y)^2-(x-y)^2=?  [#permalink]

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New post 24 Feb 2017, 07:16
Top Contributor
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 a good candidate for rephrasing the target question.
(x+y)² - (x-y)² = [x² + 2xy + y²] - [x² - 2xy + y²]
= 4xy


REPHRASED target question: What is the value of 4xy?

Statement 1: xy = 5
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

Answer: A

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Re: (x+y)^2-(x-y)^2=?  [#permalink]

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New post 24 Feb 2017, 09:48
MathRevolution wrote:
\((x+y)^2-(x-y)^2=?\)

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


\((x+y)^2-(x-y)^2==>4xy=?\)

1)x+y=5 hence 4xy==>20 -- Suff

2) x+y=6--Insuff as we don't know the value of x-y.

Hence A
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Re: (x+y)^2-(x-y)^2=?  [#permalink]

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New post 25 Feb 2017, 01:02
1
NandishSS wrote:

2) x+y=6--Insuff as we don't know the value of x-y.

Hence A


I don't think we can eliminate that answer choice just 'cause the value of (x-y) is unknown. Rather it should be because the simplied xy is unknown. Just my way of thinking :)
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Re: (x+y)^2-(x-y)^2=?  [#permalink]

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New post 25 Feb 2017, 02:31
ashwink wrote:
NandishSS wrote:

2) x+y=6--Insuff as we don't know the value of x-y.

Hence A


I don't think we can eliminate that answer choice just 'cause the value of (x-y) is unknown. Rather it should be because the simplied xy is unknown. Just my way of thinking :)


Hi ashwink,

You are right, however here we know x+y don't know about x-y. x-y can be anything...4xy comes only after simplification....if we know x-y as well then ans would be B also. :-)

Happy Prepping!!!
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Re: (x+y)^2-(x-y)^2=?  [#permalink]

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New post 26 Feb 2017, 20:25
==> If you modify the original condition and the question, \((x+y)^2-(x-y)^2=?\) becomes (x+y-x+y)(x+y+x-y)=?, and if you simplify this, you get (2y)(2x)=?, 4xy=?. Thus, for con 1), you get xy=5, hence it is unique and sufficient.

The answer is A.
Answer: A
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Re: (x+y)^2-(x-y)^2=?  [#permalink]

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Re: (x+y)^2-(x-y)^2=?   [#permalink] 02 Feb 2019, 18:47
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