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# If x^2-y^2=2, x=? (1) y^2=1 (2) x+y=1 A. Statement (1) ALONE

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Joined: 11 May 2008
Posts: 552
If x^2-y^2=2, x=? (1) y^2=1 (2) x+y=1 A. Statement (1) ALONE [#permalink]

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28 Jul 2008, 02:51
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If x^2-y^2=2, x=?
(1) y^2=1
(2) x+y=1
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Manager
Joined: 15 Jul 2008
Posts: 205

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28 Jul 2008, 03:04
X^2-Y^2=1

1). y^=1. => X^2=1 => x=1 or x=-1. Insuff.

2) x+y=1
X^2-Y^2=1 => (x+y)(x-y) =1 => x-y=1

now using x+y=1 and x-y=1, solve for x. you get x=1. sufficient.

Ans=B
SVP
Joined: 28 Dec 2005
Posts: 1500

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28 Jul 2008, 05:27
i get B as well. You do get an answer using stat 1, but there are two possible values, so its not sufficient on its own
SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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28 Jul 2008, 06:39
arjtryarjtry wrote:
If x^2-y^2=2, x=?
(1) y^2=1
(2) x+y=1
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

1)
x^2-y^2=2
--> x^2-1=2
--> x^2=3 --> x = + root (3) or - root(3)

2) x^2-y^2=2 --> (x+y)(x-y)=2
--> x-y=2 .
---> x+y=1
--> 2x=3
--> x=3/2

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Senior Manager
Joined: 19 Mar 2008
Posts: 350

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28 Jul 2008, 07:58
arjtryarjtry wrote:
If x^2-y^2=2, x=?
(1) y^2=1
(2) x+y=1
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

(1)
y^2=1
x^2 -1 = 2
x^2 = 3
x = 3^0.5 or - 3^0.5
so, Not Suff

(2) x+y=1 ---- (eq A)
x^2-y^2=2
(x+y)(x-y)=2
x-y=2
y=x-2 ---- (eq B)
Sub eq B in eq A, we got
x + x -2 = 1
2x = 3
x = 3/2
so Suff

Ans B
Re: x^2-y^2   [#permalink] 28 Jul 2008, 07:58
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# If x^2-y^2=2, x=? (1) y^2=1 (2) x+y=1 A. Statement (1) ALONE

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