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Intern  Joined: 30 Nov 2011
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Location: United States
GMAT 1: 700 Q47 V38 GPA: 3.54
If |x + 2| = 4, what is the value of x ? (1) x^2 ≠ 4 (2) x^2 = 36  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 71% (01:03) correct 29% (01:08) wrong based on 412 sessions

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If |x + 2| = 4, what is the value of x ?

(1) x^2 ≠ 4
(2) x^2 = 36

Originally posted by imadkho on 11 Mar 2012, 07:30.
Last edited by Bunuel on 19 Oct 2019, 03:04, edited 2 times in total.
Moved to PS subforum.
Math Expert V
Joined: 02 Sep 2009
Posts: 59236
Re: If |x + 2| = 4, what is the value of x ? (1) x^2 ≠ 4 (2) x^2 = 36  [#permalink]

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If |x+2|=4, what is the value of x ?

$$|x+2|=4$$ --> $$x=2$$ or $$x=-6$$.

(1) x^2 is different from 4 --> $$x^2\neq{4}$$ --> $$x\neq{2}$$ (and $$x\neq{-2}$$), so $$x=-6$$. Sufficient.

(2) x^2 = 36 --> $$x=6$$ or $$x=-6$$, so $$x=-6$$. Sufficient.

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##### General Discussion
Intern  Joined: 30 Nov 2011
Posts: 22
Location: United States
GMAT 1: 700 Q47 V38 GPA: 3.54
Re: If |x + 2| = 4, what is the value of x ? (1) x^2 ≠ 4 (2) x^2 = 36  [#permalink]

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Thanks Bunuel for your continuous assistance.
Math Expert V
Joined: 02 Sep 2009
Posts: 59236
Re: If |x + 2| = 4, what is the value of x ? (1) x^2 ≠ 4 (2) x^2 = 36  [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If |x + 2| = 4, what is the value of x ? (1) x^2 ≠ 4 (2) x^2 = 36  [#permalink]

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If |x+2|=4, what is the value of x ?
x=2, x=-6

(1) x^2 is different from 4
x^2 is different from 4
(The wording is a bit ambiguous, but I take it to mean that x^2 DOESN'T EQUAL 4)
we have two values for x, x=-6 and x=2.
When x=2, then x^2 = 4 which is invalid.
When x=-6 then x^2 = 36 which is valid.
x=6
SUFFICIENT

(2) x^2 = 36
x=-6, x=6
(plug both x values into the stem)
|x+2|=4
|-6+2|=4
|-4|=4
4=4 VALID
|x+2|=4
|6+2|=4
|8|=4
8=4 INVALID

There is only one valid answer for #2.
SUFFICIENT

(D)
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Re: If |x + 2| = 4, what is the value of x ? (1) x^2 ≠ 4 (2) x^2 = 36  [#permalink]

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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_________________ Re: If |x + 2| = 4, what is the value of x ? (1) x^2 ≠ 4 (2) x^2 = 36   [#permalink] 16 Oct 2019, 14:53
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# If |x + 2| = 4, what is the value of x ? (1) x^2 ≠ 4 (2) x^2 = 36  