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# If |x^2 − 12| = x, which of the following could be the value of x?

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If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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29 Apr 2016, 01:36
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If |x^2 − 12| = x, which of the following could be the value of x?

A. –4
B. –3
C. 1
D. 2
E. 3
[Reveal] Spoiler: OA

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Re: If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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29 Apr 2016, 01:46
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Bunuel wrote:
If |x^2 − 12| = x, which of the following could be the value of x?

A. –4
B. –3
C. 1
D. 2
E. 3

Hi,
In MODULUS, always be careful of EQUATING two sides..

Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE..
A and B are eliminated..
Now try to substitute remaining choices
C. 1
|x^2 − 12| = x..
|1^2-12|=1.. 11=1.. NO

D. 2
|x^2 − 12| = x..
|2^2-12|=2.. 7=2.. NO

E. 3
|x^2 − 12| = x..
|3^2-12|=3.. 3=3.. YES

ans E
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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29 Apr 2016, 02:01
Another easy way and time-saver will be to substitute the values directly in the equation.
so
A: |(-4)^2-12|=|4| ne -4 => FALSE
B: |(-3)^2-12|=|-3| ne -3 => FALSE
C: |(1)^2-12|=|-11| ne -1 => FALSE
D: |(2)^2-12|=|-8| ne 2=> FALSE
E: |(3)^2-12|=|-3| eq 3 => TRUE
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Re: If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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29 Apr 2016, 11:14
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well, a mod here indicates that x is positive.
Eliminate a and b immediately.
Now, you may substitute values themselves..none of them except E fits the bill.

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Re: If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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29 Apr 2016, 11:52
Another easy way and time-saver will be to substitute the values directly in the equation.
so
A: |(-4)^2-12|=|4| ne -4 => FALSE
B: |(-3)^2-12|=|-3| ne -3 => FALSE
C: |(1)^2-12|=|-11| ne -1 => FALSE
D: |(2)^2-12|=|-8| ne 2=> FALSE
E: |(3)^2-12|=|-3| eq 3 => TRUE

Substituting the value works in most of the Problems of GMAT and is a sureshot way...

Same opinion , answer will be (E)
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If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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25 Jul 2016, 01:23
1
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Bunuel wrote:
If |x^2 − 12| = x, which of the following could be the value of x?

A. –4
B. –3
C. 1
D. 2
E. 3

$$|x^2 − 12| = x$$
$$|x^2 − 12|$$cannot be negative; anything that comes out of mod is always positive
so $$|x^2 − 12|>0$$

Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0

Now only Option C=1 or D=2 or E=3 are contenders for right answers.

A quick Cursory crude calculation will tell you that E is the right choice
$$|-3^2-12|=3$$

$$|9-12|=3$$

$$|-3|=3$$

$$3=3$$

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Re: If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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27 Nov 2017, 13:27
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Re: If |x^2 − 12| = x, which of the following could be the value of x?   [#permalink] 27 Nov 2017, 13:27
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