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# What is the value of x ?

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What is the value of x ? [#permalink]

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01 Mar 2012, 00:31
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What is the value of x ?

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

[Reveal] Spoiler: OA
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Re: What is the value of x ? [#permalink]

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01 Mar 2012, 00:59
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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.

Hope it's clear.
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Re: What is the value of x ? [#permalink]

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01 Mar 2012, 08:32
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]

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01 Mar 2012, 08:58
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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Re: What is the value of x ? [#permalink]

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01 Mar 2012, 09:04
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]

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01 Mar 2012, 09:42
@ Bunuel

Thanks for correction
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Re: What is the value of x ? [#permalink]

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22 Sep 2015, 01:08
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: What is the value of x ? [#permalink]

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22 Sep 2015, 03:33
wizard wrote:
What is the value of x ?

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

Required: x =?

Statement 1: $$x^2 + y^2 = 25$$
We have one equation and two unknowns. Hence we cannot solve this equaiton.

INSUFFICIENT

Statement 2: xy = 12
Again, we have one equation and two unknowns. Hence we cannot solve this equaiton.

INSUFFICIENT

Statement 1 and Statement 2 combined:
$$x^2 + y^2 = 25$$ and xy = 12

Whenever we have something of the form $$x^2 +/- y^2$$ , try to make it into perfect squares.
We know that $$(x+y)^2 = x^2 + y^2 +2xy$$
So, we need the value of xy to make statement 1 a perfect square and we have the value of xy from statement 2.

Adding 2xy = 24 on both sides in statement 1, we have
$$x^2 + y^2 +2xy = 49$$
or $$(x+y)^2 = 7^2$$
Still we cannot solve for the value of x

INSUFFICIENT
Option E is the correct answer
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Re: What is the value of x ? [#permalink]

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16 Sep 2016, 18:12
E is correct. Here's why:

(1) x^2 + y^2 = 25 --> If you remember pythagorean triplets (i.e. one being 3-4-5 triangle). Using this as an example, we have no way of knowing what value x takes on... +/- 3 or +/- 4. Thus, INSUFFICIENT

(2) xy = 12 --> We have no way of knowing what value x takes on. Thus, INSUFFICIENT

...so A, B, and D are out at this point

Trying (1) + (2) together, we still do not have any way of knowing with certainty the value of x. Thus, A,B,C,D are out.
Re: What is the value of x ?   [#permalink] 16 Sep 2016, 18:12
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