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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: 59712
If x + y = 7 and x – y = 3, then x^2 - y^2 =  [#permalink]

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31 Mar 2016, 00:57
1
3
00:00

Difficulty:

5% (low)

Question Stats:

94% (00:37) correct 6% (00:38) wrong based on 249 sessions

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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

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Intern
Joined: 03 Mar 2013
Posts: 37
Re: If x + y = 7 and x – y = 3, then x^2 - y^2 =  [#permalink]

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31 Mar 2016, 04:19
1
1
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

Senior Manager
Joined: 20 Aug 2015
Posts: 384
Location: India
GMAT 1: 760 Q50 V44
If x + y = 7 and x – y = 3, then x^2 - y^2 =  [#permalink]

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31 Mar 2016, 05:07
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
Intern
Joined: 29 Feb 2016
Posts: 9
Schools: Mannheim
GMAT 1: 670 Q44 V39
GPA: 3.3
Re: If x + y = 7 and x – y = 3, then x^2 - y^2 =  [#permalink]

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31 Mar 2016, 05:09
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

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Joined: 12 Sep 2015
Posts: 4145
Re: If x + y = 7 and x – y = 3, then x^2 - y^2 =  [#permalink]

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31 Mar 2016, 07:21
1
1
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

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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Director
Joined: 12 Nov 2016
Posts: 694
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: If x + y = 7 and x – y = 3, then x^2 - y^2 =  [#permalink]

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31 Aug 2017, 17:02
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
Posts: 13743
Re: If x + y = 7 and x – y = 3, then x^2 - y^2 =  [#permalink]

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07 Feb 2019, 19:00
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 =   [#permalink] 07 Feb 2019, 19:00
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