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# What is the value of x?

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What is the value of x? [#permalink]  18 Dec 2012, 21:59
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Difficulty:

35% (medium)

Question Stats:

71% (01:43) correct 29% (00:59) wrong based on 51 sessions
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, 07:12, edited 1 time in total.
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Kudos [?]: 858 [1] , given: 116

Re: What is the value of x? [#permalink]  18 Dec 2012, 22:34
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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, 01:39
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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, 01:44
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Expert's post
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, 01:44
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# What is the value of x?

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