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# What is the value of x^2 – y^2 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 46167
What is the value of x^2 – y^2 ? [#permalink]

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24 Jun 2017, 08:34
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Difficulty:

55% (hard)

Question Stats:

68% (01:05) correct 32% (01:52) wrong based on 81 sessions

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What is the value of $$x^2 – y^2$$ ?

(1) $$(x – y)(2x + y) = 9$$

(2) $$y(x – y) = 3$$

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Manager
Joined: 04 Apr 2015
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Re: What is the value of x^2 – y^2 ? [#permalink]

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24 Jun 2017, 10:57
IMO C

From both we can find that x=4y
putting value back to statement 2 will give y=+/- 1

since we are asked square of x - square of y, no matter what the sign we will get the same result.

waiting for OA
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Joined: 31 Dec 2012
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Re: What is the value of x^2 – y^2 ? [#permalink]

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24 Jun 2017, 11:46

From Statement 1, (x–y)(2x+y)=9 => 2x^2-xy-y^2 = 9. Clearly Insufficient.

From Statement 2, y(x–y)=3 => xy-y^2 = 3. Clearly Insufficient.

Combining Both statement, i.e substituting statement 2 in statement 1,

xy = 3+y^2 ------ from statement 2,

2x^2-(3+y^2)-y^2 = 9 => 2x^2-2y^2=12,

Solving, x^2-y^2 = 6. Hence, Answer C.
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Re: What is the value of x^2 – y^2 ? [#permalink]

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21 Sep 2017, 23:44
1
C.

Stmt-1: $$(x-y)(2x+y)=9$$

Stmt-2: $$y(x-y)=3 => 3y(x-y)=9$$ (Multiplied both sides by 3)

From stmt 1 and 2, we can say
$$3y(x-y)=(x-y)(2x+y) => 3y=(2x+y) => x=y$$

$$∴ x^2 – y^2=0$$
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Hasan Mahmud

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Joined: 20 Sep 2017
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Re: What is the value of x^2 – y^2 ? [#permalink]

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22 Sep 2017, 00:30
(1) Unsuf.
(2) Unsuf.
(1) & (2) х=у but it doesn't satisfy (1) (0=9)
Unsuf.
Re: What is the value of x^2 – y^2 ?   [#permalink] 22 Sep 2017, 00:30
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