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# If xy = 7 and x – y = 7, then x² +

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Joined: 12 Sep 2015
Posts: 4007
If xy = 7 and x – y = 7, then x² +  [#permalink]

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17 Feb 2017, 09:55
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Difficulty:

35% (medium)

Question Stats:

65% (01:21) correct 35% (01:56) wrong based on 193 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

* Kudos for all correct solutions

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

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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

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

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17 Feb 2017, 10:13
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1
(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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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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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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16 Jul 2017, 13:09
If xy = 7 and x – y = 7, then x² + y² =

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

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

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

$$x^2 + y^2 = 49 + 14$$

$$x^2 + y^2 = 63$$

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

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19 Sep 2019, 07:16
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Re: If xy = 7 and x – y = 7, then x² +   [#permalink] 19 Sep 2019, 07:16
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