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555-605 Level|   Algebra|      
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BrentGMATPrepNow
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If xy = 7 and x – y = 7, then x² + 17 Feb 2017, 09:55
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

68% (01:19) correct 32% (01:50) wrong based on 433 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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E
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BrentGMATPrepNow
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If xy = 7 and x – y = 7, then x² + Updated on: 13 Nov 2019, 17:08
Originally posted by BrentGMATPrepNow on 22 Mar 2017, 14:43.
Last edited by BrentGMATPrepNow on 13 Nov 2019, 17:08, edited 1 time in total.
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GMATPrepNow
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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If xy = 7 and x – y = 7, then x² + 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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If xy = 7 and x – y = 7, then x² + 22 Mar 2017, 18:34
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GMATPrepNow
If xy = 7 and x – y = 7, then x² + y² =

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

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x² + y²=(x-y)²+2xy
=7²+2*7
=49+14
=63
So, the correct choice is
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E
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If xy = 7 and x – y = 7, then x² + 23 Mar 2017, 08:47
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GMATPrepNow
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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If xy = 7 and x – y = 7, then x² + 16 Jul 2017, 13:09
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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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If xy = 7 and x – y = 7, then x² + 04 Aug 2020, 23:40
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BrentGMATPrepNow
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

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

\((x - y)^2 = x^2 + y^2 -2xy\)
\(49 = x^2 + y^2 - 14\)
\(x^2 + y^2 = 49 + 14 = 63\)

IMO E
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If xy = 7 and x – y = 7, then x² + 16 Oct 2021, 11:31
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BrentGMATPrepNow
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

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

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

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

Or, \(x^2 + y^2 = 63\), Answer must be (E)
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If xy = 7 and x – y = 7, then x² + 18 Jan 2024, 02:32
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