If x + y = 7 and x – y = 3, then x^2 - y^2 = : Problem Solving (PS)

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If x + y = 7 and x – y = 3, then x^2 - y^2 =

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Math Expert

Joined: 02 Sep 2009

Posts: 52906

If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink]

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30 Mar 2016, 23:57

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5% (low)

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94% (00:37) correct

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If x + y = 7 and x – y = 3, then x^2 - y^2 =

A. -4
B. 4
C. 10
D. 21
E. 40

Spoiler: OA

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Joined: 03 Mar 2013

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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink]

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31 Mar 2016, 03:19

Bunuel wrote:

If x + y = 7 and x – y = 3, then x^2 - y^2 =

Well, x^2-y^2 = (x + y)(x - y)

substituting each of (x + y) and (x - y) with 7 and 3, respectively as per above, then

x^2-y^2 = 7*3 = 21

Answer is D

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If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink]

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31 Mar 2016, 04:07

Bunuel wrote:

If x + y = 7 and x – y = 3, then x^2 - y^2 =

A. -4
B. 4
C. 10
D. 21
E. 40

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

Putting the values in the equation:
\(x^2 - y^2 = 7*3 = 21\)
Option D

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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink]

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31 Mar 2016, 04:09

Bunuel wrote:

If x + y = 7 and x – y = 3, then x^2 - y^2 =

A. -4
B. 4
C. 10
D. 21
E. 40

x - y = 3
-> x = 3 + y

put this in the other equation ( x + y = 7):

3 + y + y = 7
-> 2y = 4 -> y = 2

Put y in the first equation (x - y = 3):

x - 2 = 3
-> x = 5

Therefore: x^2 - y^2 = 5^2 - 2^2 = 25 - 4 = 21

Answer: D
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink]

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31 Mar 2016, 06:21

Bunuel wrote:

If x + y = 7 and x – y = 3, then x² - y² =

A. -4
B. 4
C. 10
D. 21
E. 40

The fastest approach has already been shown. Here's one more option.

Given:
x + y = 7
x – y = 3
Add the two equations to get: 2x = 10, which means x = 5
If x = 5, we can plug that value into either equation, to conclude that y = 2

If x = 5 and y = 2, then x² - y² = 5² - 2² = 25 - 4 = 21
Answer: D

RELATED RESOURCES (free videos) FOR SOLVING THIS QUESTIONS
- Solving 2 equations with 2 unknowns: https://www.gmatprepnow.com/module/gmat ... /video/966
- Difference of square factoring: https://www.gmatprepnow.com/module/gmat ... /video/955

Cheers,
Brent
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink]

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31 Aug 2017, 16:02

Bunuel wrote:

If x + y = 7 and x – y = 3, then x^2 - y^2 =

A. -4
B. 4
C. 10
D. 21
E. 40

pick numbers

5 +2 =7

5-2= 3

25-4= 21

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Joined: 09 Sep 2013

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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink]

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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] 07 Feb 2019, 18:00

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