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# What is the value of x ?

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General Discussion
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Re: What is the value of x ? [#permalink]
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]
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]
@ Bunuel

Thanks for correction
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Re: What is the value of x ? [#permalink]
1
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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]
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.
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Re: What is the value of x ? [#permalink]
wizard wrote:
What is the value of x ?

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

(1) x^2 + y^2 = 25
x can take multiple values. Eg: x=3, y=4 OR x=4, y=3 OR x=-3, y=4.. and so on. x and y can both take positive as well as negative values also. Insufficient.

(2) xy = 12.
Here also x can take multiple values. Eg: x=4, y=3 Or x=-4,y=-3. x and y can take mutliple values, though both x/y will have same sign. Insufficient.

Combining the two statements, x/y both have same sign, but still more than one cases possible. Eg, x=4,y=3 OR x=-4,y=-3 etc. Insufficient.
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Re: What is the value of x ? [#permalink]
(1) (x^2) + (y^2) = 25 . Insufficient
Different values of x

(2) xy = 12 . Insufficient
x can be 3,4,6 etc.

Combining both, Insufficient
x can be 3 or 4 or -3 or -4

Hence, OA is (E).
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Re: What is the value of x ? [#permalink]
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Re: What is the value of x ? [#permalink]
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