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What is the value of x ?

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What is the value of x ? [#permalink] New post 29 Feb 2012, 23:31
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (01:43) correct 16% (00:30) wrong based on 31 sessions
What is the value of x ?

(1) (x^2) + (y^2) = 25
(2) xy = 12

Thanks for your help.
[Reveal] Spoiler: OA
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Re: What is the value of x ? [#permalink] New post 29 Feb 2012, 23:59
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What is the value of x ?

(1) x^2 + y^2 = 25. Two unknowns, hence can not get the value of x. Not sufficient.
(2) xy = 12. Two unknowns, hence can not get the value of x. Not sufficient.

(1)+(2) Now, we can go strictly algebraic way, though I'd suggest the following: x^2 + y^2 = 5^2 always makes me think about Pythagorean triple (3, 4, 5): 3^2+4^2=5^2. Now, 3 and 4 fit perfectly in xy = 12 too, so x can be 3 or 4. Moreover if we take the sign into consideration then there are even more options for (x, y): (3, 4); (4, 3); (-3, -4); (-4, -3). So, we have 4 possible values of x. Not sufficient.

Answer: E.

Hope it's clear.
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Re: What is the value of x ? [#permalink] New post 01 Mar 2012, 07:32
x=?
a) x^2 + y^2 = 25
x^2+ y^2 = 5^2
but we cannot deduce value of x ---NS

b) x*y = 12
Clearly not sufficient

a+b) x^2+y^2+2xy= (x+y)^2

25+24= (x+y)^2
7 = x+y
need y to calculate X --NS
E
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Re: What is the value of x ? [#permalink] New post 01 Mar 2012, 07:58
Expert's post
GMATD11 wrote:
x=?
a) x^2 + y^2 = 25
x^2+ y^2 = 5^2
but we cannot deduce value of x ---NS

b) x*y = 12
Clearly not sufficient

a+b) x^2+y^2+2xy= (x+y)^2

25+24= (x+y)^2
7 = x+y
need y to calculate X --NS
E


From (x+y)^2=49 --> x+y=7 or x+y=-7. Also, the point is not that we need y to calculate x, but that we can get 4 different values of y from this system of equation, which give 4 different values of x.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What is the value of x ? [#permalink] New post 01 Mar 2012, 08:04
Seemed simpler than it actually is... I almost feel for C in first 10 seconds.

Good question!
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Re: What is the value of x ? [#permalink] New post 01 Mar 2012, 08:42
@ Bunuel

Thanks for correction
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Re: What is the value of x ?   [#permalink] 01 Mar 2012, 08:42
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