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If xy = 7 and x – y = 7, then x² +

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If xy = 7 and x – y = 7, then x² +  [#permalink]

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New post 17 Feb 2017, 09:55
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Question Stats:

65% (01:06) correct 35% (01:25) wrong based on 164 sessions

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If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

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Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

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New post 17 Feb 2017, 10:13
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(x-y)^2= x^2 + y^2 - 2xy
7^2 = x^2 + y^2 -2*7
x^2 + y^2 = 49+14
x^2 + y^2 = 63

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Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

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New post 22 Mar 2017, 14:43
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GMATPrepNow wrote:
If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63


The important thing to recognize here is that if we square (x - y), we get a x² term and a y² term. We also get an extra xy term, but that's okay, because we're given some information about the product xy.

So, take: x – y = 7 and...
Square both sides: (x - y)² = 7²
Expand: x² - 2xy + y² = 49
Since we're told xy = 7, we'll replace xy with 7 to get: x² - 2(7) + y² = 49
Simplify: x² - 14 + y² = 49
Add 14 to both sides: x² + y² = 63

Answer: E

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Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

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New post 22 Mar 2017, 18:34
GMATPrepNow wrote:
If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

* Kudos for all correct solutions

x² + y²=(x-y)²+2xy
=7²+2*7
=49+14
=63
So, the correct choice is
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Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

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New post 23 Mar 2017, 08:47
GMATPrepNow wrote:
If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

* Kudos for all correct solutions


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

Or, \(7^2 + 2*7 = x^2 + y^2\)

Or, \(49 + 14 = x^2 + y^2\)

Or, \(x^2 + y^2 = 63\)

Thus, answer must be (E) 63...
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Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

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New post 16 Jul 2017, 13:09
If xy = 7 and x – y = 7, then x² + y² =

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

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

\(x^2 + y^2 = (7)^2 + 2 * 7\)

\(x^2 + y^2 = 49 + 14\)

\(x^2 + y^2 = 63\)

Hence, Answer is E

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Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

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New post 23 Aug 2018, 11:44
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