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# If x² - y² = 55, and x - y = 11, then y =

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Math Expert
Joined: 02 Sep 2009
Posts: 51229
If x² - y² = 55, and x - y = 11, then y =  [#permalink]

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12 May 2016, 00:58
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

82% (01:20) correct 18% (02:01) wrong based on 154 sessions

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If x^2 - y^2 = 55, and x - y = 11, then y =

A. 8
B. 5
C. 3
D. -8
E. -3

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Joined: 07 May 2016
Posts: 26
If x² - y² = 55, and x - y = 11, then y =  [#permalink]

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Updated on: 12 May 2016, 07:18
1
Bunuel wrote:
If x^2 - y^2 = 55, and x - y = 11, then y =

A. 8
B. 5
C. 3
D. -8
E. -3

Hi
we have x - y = 11
=> x = 11+y
replace x into the first equation
=>$$(11+y)^2 - y^2 = 55$$
EXPANDING:
=>$$(11)^2 + 2*(11)*y + y^2 - y^2 = 55$$
=>$$121 + 22y = 55$$
=>$$22y = 55 - 121$$
=>$$22y = -66$$
=>$$y = -66/22 = -3$$

Originally posted by HungNguyen on 12 May 2016, 06:10.
Last edited by HungNguyen on 12 May 2016, 07:18, edited 1 time in total.
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Re: If x² - y² = 55, and x - y = 11, then y =  [#permalink]

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12 May 2016, 06:56
Bunuel wrote:
If x^2 - y^2 = 55, and x - y = 11, then y =

A. 8
B. 5
C. 3
D. -8
E. -3

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

$$55$$ = $$( 11 )( x + y )$$

$$5$$ = $$x + y$$-------> (1)

$$11$$ = $$x - y$$-------> (2)

$$2x$$ = $$16$$

Or, $$x$$ = $$8$$

SO,$$y$$ = $$-3$$

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Re: If x² - y² = 55, and x - y = 11, then y =  [#permalink]

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12 May 2016, 10:29
(x+y)(x-y)= 55

x+y= 5 (its given that (x-y)= 11)

Solving two equations:-

x+y=5
x-y=11

y= -3
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Re: If x² - y² = 55, and x - y = 11, then y =  [#permalink]

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15 Oct 2017, 08:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x² - y² = 55, and x - y = 11, then y = &nbs [#permalink] 15 Oct 2017, 08:49
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