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# If |x – 6| = 5, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 47099
If |x – 6| = 5, what is the value of x? [#permalink]

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02 Dec 2016, 06:50
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35% (medium)

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57% (00:46) correct 43% (00:38) wrong based on 154 sessions

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If |x – 6| = 5, what is the value of x?

(1) x > 0
(2) x^2 = 121

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Director
Joined: 05 Mar 2015
Posts: 980
Re: If |x – 6| = 5, what is the value of x? [#permalink]

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02 Dec 2016, 07:43
1
Bunuel wrote:
If |x – 6| = 5, what is the value of x?

(1) x > 0
(2) x^2 = 121

|x – 6| = 5
means x-6=5 or x-6=-5
solving both x=11 or 1----(a)

(1) x=11 , 1....not suff..
(2) x=11 , -11
but from (a) x= 11,1
thus x=11---------> suff

Ans B
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Joined: 02 Nov 2013
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Location: India
Re: If |x – 6| = 5, what is the value of x? [#permalink]

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02 Dec 2016, 09:17
If |x – 6| = 5
By removing the modulus we will have,
x-6 = 5 or x-6=-5. It will have two values of X i.e. 1 and 11.
Coming to options,
Option 1: x>0. As both the values are greater than 0. Option is not sufficient.
Option 2: x^2 = 121. X will have two values either 11 or -11. Sufficient.

Intern
Joined: 04 Sep 2017
Posts: 14
Re: If |x – 6| = 5, what is the value of x? [#permalink]

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15 Mar 2018, 04:29
Can someone explain to me how the answer is B?

Statement 2 gives us two answers: -11 and 11, therefore it should be NS.

If we combine both statements we get 11. So shouldnt the answer be C?
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Re: If |x – 6| = 5, what is the value of x? [#permalink]

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15 Mar 2018, 04:33
1
teamryan15 wrote:
Can someone explain to me how the answer is B?

Statement 2 gives us two answers: -11 and 11, therefore it should be NS.

If we combine both statements we get 11. So shouldnt the answer be C?

Hi teamryan15 ,

Answer is B because even though you got x = 11 or -11, only x = 11 will satisfy the original condition given |x-6| = 5.

Does that make sense?
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Joined: 04 Sep 2017
Posts: 14
Re: If |x – 6| = 5, what is the value of x? [#permalink]

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15 Mar 2018, 04:43
abhimahna wrote:
teamryan15 wrote:
Can someone explain to me how the answer is B?

Statement 2 gives us two answers: -11 and 11, therefore it should be NS.

If we combine both statements we get 11. So shouldnt the answer be C?

Hi teamryan15 ,

Answer is B because even though you got x = 11 or -11, only x = 11 will satisfy the original condition given |x-6| = 5.

Does that make sense?

It does. Looks like I should have read the question stem more closely.
Intern
Joined: 09 May 2015
Posts: 5
Re: If |x – 6| = 5, what is the value of x? [#permalink]

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20 Mar 2018, 03:59
i am still unable to understand why the answer is not D but B.
We should check for both the negative and positive values of x.For x<0,-(x-6)=5 or -x+6=5 or x=1.hence not satisfied.
For x>0,(x-6)=5 or x=11.
from statement 1: only x=11 will satisfy the value.
from statement 2 also: x=11 will satisfy the value.
hence D.
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If |x – 6| = 5, what is the value of x? [#permalink]

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20 Mar 2018, 04:05
1
kuldeepdubai1986 wrote:
i am still unable to understand why the answer is not D but B.
We should check for both the negative and positive values of x.For x<0,-(x-6)=5 or -x+6=5 or x=1.hence not satisfied.
For x>0,(x-6)=5 or x=11.
from statement 1: only x=11 will satisfy the value.
from statement 2 also: x=11 will satisfy the value.
hence D.

Hey kuldeepdubai1986 ,

You missed very important point of modulus.

|x - 6 | = x - 6 if x >= 6
|x - 6 | = -(x-6) if x < 6

Now, in option A. We are told x > 0. That could mean x could be 1,2 or value more than 6.

Hence, when you open the modulus, you will get

|x-6| = 5

x-6 = 5 => x = 11

or -(x-6) = 5 => -x+6=5 => x = 1

Hence, two values of x for x > 0. Therefore, A is insufficient.

Does that make sense?
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Re: If |x – 6| = 5, what is the value of x? [#permalink]

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21 Mar 2018, 21:19
Bunuel wrote:
If |x – 6| = 5, what is the value of x?

(1) x > 0
(2) x^2 = 121

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

$$|x-6| = 5$$
$$⇔ x-6 = ±5$$
$$⇔ x = 6 ±5$$
$$⇔ x = 11$$ or $$x = 1$$

Condition 1)
Since we have $$x = 11$$ or $$x = 1$$ from $$x > 0$$, we don't have a unique solution.
Thus condition 1) is not sufficient.

Condition 2)
$$x^2 = 121$$
$$⇔ x = ± 11$$
Since we have a solution 11 only, condition 2) is sufficient.

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Re: If |x – 6| = 5, what is the value of x?   [#permalink] 21 Mar 2018, 21:19
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