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# If |x + 3| = 3, what is the value of x? (1) x^2 ≠ 0 (2) x^2 + 6x = 0

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Joined: 02 Sep 2009
Posts: 64068
If |x + 3| = 3, what is the value of x? (1) x^2 ≠ 0 (2) x^2 + 6x = 0  [#permalink]

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21 Sep 2018, 00:41
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35% (medium)

Question Stats:

64% (01:06) correct 36% (01:19) wrong based on 157 sessions

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If |x + 3| = 3, what is the value of x?

(1) x^2 ≠ 0
(2) x^2 + 6x = 0

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Re: If |x + 3| = 3, what is the value of x? (1) x^2 ≠ 0 (2) x^2 + 6x = 0  [#permalink]

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21 Sep 2018, 00:53
1
Bunuel wrote:
If |x + 3| = 3, what is the value of x?

(1) x^2 ≠ 0
(2) x^2 + 6x = 0

|x + 3| = 3 i.e. x = 0 or -6

Question: what is the value of x?

Statement 1: x^2 ≠ 0
i.e. x ≠ 0
i.e. x = -6

SUFFICIENT

Statement 2: x^2 + 6x = 0
i.e. x (x+6) = 0
i.e. x = -6 or 0

NOT SUFFICIENT

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Re: If |x + 3| = 3, what is the value of x? (1) x^2 ≠ 0 (2) x^2 + 6x = 0  [#permalink]

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21 Sep 2018, 05:03
Top Contributor
Bunuel wrote:
If |x + 3| = 3, what is the value of x?

(1) x² ≠ 0
(2) x² + 6x = 0

Target question: What is the value of x?

Given: |x + 3| = 3
This means that EITHER x + 3 = 3 OR x + 3 = -3
If x + 3 = 3, then x = 0
If x + 3 = -3, then x = -6
So, EITHER x = 0 OR x = -6

Statement 1: x² ≠ 0
This tells us that x does not equal 0
Since we also know that EITHER x = 0 OR x = -6, we can be certain that x = -6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x² + 6x = 0
Factor to get (x)(x + 6) = 0
This tells us that EITHER x = 0 OR x = -6
This doesn't help us at all, since we ALREADY knew that EITHER x = 0 OR x = -6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Re: If |x + 3| = 3, what is the value of x? (1) x^2 ≠ 0 (2) x^2 + 6x = 0  [#permalink]

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16 Feb 2019, 23:35
Bunuel wrote:
If |x + 3| = 3, what is the value of x?

(1) x^2 ≠ 0
(2) x^2 + 6x = 0

So even we solve for the if statement we get 2 solutions i.e. 0 or -6

from 1) x^2 ≠ 0, means only -6 can work here
Sufficient

from 2) we get 2 values
x = 0 or x = -6

Out of which one value will give us a Yes, and other one will give us a No

Insufficient
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Re: If |x + 3| = 3, what is the value of x? (1) x^2 ≠ 0 (2) x^2 + 6x = 0   [#permalink] 16 Feb 2019, 23:35