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If x + y = 7 and x – y = 3, then x^2 - y^2 =
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Bunuel
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If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post  30 Mar 2016, 23:57
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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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BrentGMATPrepNow
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If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post  Updated on: 22 Feb 2021, 10:30
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Bunuel wrote:
If x + y = 7 and x – y = 3, then x² - y² =

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


APPROACH #1: Factor the difference of squares
Key property: \((a^2 - b^2)=(a+b)(a-b)\)

So, \((x^2 - y^2)=(x+y)(x-y)\)
\(=(7)(3)\)
\(=21\)

Answer: D

APPROACH #2: Solve the system of equations
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

Cheers,
Brent
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Originally posted by BrentGMATPrepNow on 31 Mar 2016, 06:21.
Last edited by BrentGMATPrepNow on 22 Feb 2021, 10:30, edited 2 times in total.
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InstantMBA
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post  31 Mar 2016, 03:19
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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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TeamGMATIFY
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If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post  31 Mar 2016, 04:07
Expert Reply
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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Kocket
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post  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] New post  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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Sabby
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post  04 Dec 2020, 17:08
x+y =7 and x-y=3
therefore : x+y+x-y=7+3=10
2x=10 => x=5 as x+y=7 => 5+y=7 => y=2

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]
04 Dec 2020, 17:08
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