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Math Expert V
Joined: 02 Sep 2009
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What is the value of x? (1) (-x)^3 = -x^3 (2) (-x)^2 = -x^2  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 58% (01:17) correct 42% (01:05) wrong based on 124 sessions

HideShow timer Statistics What is the value of x?

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

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Re: What is the value of x? (1) (-x)^3 = -x^3 (2) (-x)^2 = -x^2  [#permalink]

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1
Statement 1) $$-x^3 = -x^3$$. INSUFFICIENT
Statement 2) $$x^2 = -x^2$$

$$2x^2$$ = 0 => x = 0. SUFFICIENT

OPTION: B
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Re: What is the value of x? (1) (-x)^3 = -x^3 (2) (-x)^2 = -x^2  [#permalink]

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Bunuel wrote:
What is the value of x?

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

Statement 1:

$$(-x)^3 = -x^3$$

$$-x^3 = -x^3$$

$$x^3 = x^3$$

x could be 10, o , 100.

NOT sufficient.

Statement 2;

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

$$x^2 = -x^2$$

It only possible when x = 0.

Sufficient.

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Re: What is the value of x? (1) (-x)^3 = -x^3 (2) (-x)^2 = -x^2  [#permalink]

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Math Expert V
Joined: 02 Sep 2009
Posts: 55801
Re: What is the value of x? (1) (-x)^3 = -x^3 (2) (-x)^2 = -x^2  [#permalink]

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Bunuel wrote:
What is the value of x?

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

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Joined: 24 Dec 2018
Posts: 48
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GMAT 1: 710 Q47 V40 Re: What is the value of x? (1) (-x)^3 = -x^3 (2) (-x)^2 = -x^2  [#permalink]

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I think the trap in this question lies in tricking you to think that statement 2 will also give a similar solution as statement 1 did. This tends to happen in a lot of DS questions with seemingly similar statements.

Lets dive in!

Statement 1: $$(-x)^3 = -x^3$$

An odd power does not change the sign of a number.

So, whether x is positive or negative or 0, $$(-x)^3$$ will always be equal to $$-x^3$$. To illustrate this point, lets take examples:

Case 1: x is 1

$$(-1)^3 = -1^3$$ which is essentially -1

Case 2: x is 0

$$(-0)^3 = -0^3$$ which is essentially 0

Case 3: x is -1

$$(--1)^3 = --1^3$$ which is essentially 1

Since we get no unique value for x, this statement is insufficient

Statement 2: Even power of a number always changes the sign of a number to non-negative.

Thus, $$(-x)^2$$ will be equal to $$x^2$$
Thus, expression translates to: $$x^2 = -x^2$$
Which implies: $$2x^2 = 0$$
Which implies x=0.

Hence, statement 2 is sufficient and answer is B
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Hit Kudos if you like my answer! Re: What is the value of x? (1) (-x)^3 = -x^3 (2) (-x)^2 = -x^2   [#permalink] 29 Dec 2018, 12:59
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