What is the value of x?

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What is the value of x? [#permalink]

18 Dec 2012, 22:59

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What is the value of x?

(1) x^3 - x^2 = 0
(2) (-x)^2 = -x^2

[Reveal] Spoiler: OA

Last edited by jsphcal on 19 Dec 2012, 08:12, edited 1 time in total.

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

18 Dec 2012, 23:34

jsphcal wrote:

What is the value of x?

(1) x^3 - x^2 = 0

(2) (-x)^2 = -x^2

1) x can be either 0 or 1. Insufficient.

2) Lets say x^2 = a. We are given a = -a. So, a can only be 0 and hence x can only be 0.

Answer is B
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Re: What is the value of x? [#permalink]

19 Dec 2012, 02:39

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jsphcal wrote:

What is the value of x?

(1) x^3 - x^2 = 0

(2) (-x)^2 = -x^2

In this case, it is better to simplify. This is a "value" question, so our answer depends on finding the exact value of x.

(1)

x^3-x^2=0
x^2(x-1)=0
=> either x=0 or x=1
INSUFFICIENT

(2)

(-x)^2 = -x^2
Simplifying left hand side,

(-x)^2 = (-1*x)^2 = (-1)^2 * (x)^2 = x^2

Thus the original expression is reduced to x^2=-x^2, which can only happen when x=0.
SUFFICIENT

Thus the answer is B.
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Re: What is the value of x? [#permalink]

19 Dec 2012, 02:44

What is the value of x?

(1) x^3 - x^2 = 0 --> x^2(x-1)=0 --> x=0 or x=1. Not sufficient.

(2) (-x)^2 = -x^2 --> x^2=-x^2 --> 2x^2=0 --> x=0. Sufficient.

Answer: B.
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Re: What is the value of x? [#permalink] 19 Dec 2012, 02:44

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