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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, 02:36
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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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Posts: 5732
Re: If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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29 Apr 2016, 02:46
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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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Re: If |x^2 − 12| = x, which of the following could be the value of x? [#permalink]

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29 Apr 2016, 03:01
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, 12:14
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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, 12:52
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, 02:23
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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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12 Mar 2018, 05:12
chetan2u wrote:
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

Hi chetan2u,

Though I know the substitution method, but instinctively I went to solve the the equations given.

Can you help me how it can be done with critical value method. I am stuck up.
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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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12 Mar 2018, 10:36
Abhishek009 wrote:
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)

Can you tell me the algebraic way?

I am stuck up a bit.

QZ
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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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13 Mar 2018, 16:57
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

Since we see that the left side of the equation must be positive, the right side also must be positive.

Thus, A and B cannot be correct since the absolute value of any quantity can’t be negative. Let’s substitute in the remaining answer choices:

|1^2 - 12 | = 1 ?

We see this is not true.

|2^2 - 12| = 2 ?

We see this is not true

|3^3 - 12| = 3 ?

We see this is 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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13 Mar 2018, 18:01
QZ wrote:
Abhishek009 wrote:
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)

Can you tell me the algebraic way?

I am stuck up a bit.

QZ

I'll help.

First of all, x is the outcome of an absolute value so x=>0

Then we have to analyze the two possible scenarios of what we have inside the absolute value so that we can eliminate the absolute value:

1. X^2-12=>0, x^2=>12
So that x=<-sqrt(12) or x=>sqrt(12)
The only possible scenario according to the constraint that x can take any non negative value is the second one so we can say that x has to be greater than or equal to approximately 3.4

Then we would have the quadratic equation x^2-x-12=0 with roots x=-3 or x=4 we eliminate the first one because x can not take negative values.

2. X^2-12<0, x^2<12
So that -sqrt(12)<x<sqrt(12)
Then according to the initial constraint 0<x<3.4

Then we would have the quadratic equation x^2+x-12=0 with roots x=3 or x=-4
We eliminate the second one because x can not take negative values.

So from the first scenario x=4 and from the second one x=3, those are the two solutions for the absolute value equation.

I hope it is clear.

Regards

César Orihuela

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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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20 Mar 2018, 22:05
Thanks Cesar to clarify.

Posted from my mobile device
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Re: If |x^2 − 12| = x, which of the following could be the value of x?   [#permalink] 20 Mar 2018, 22:05
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