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Math Expert V
Joined: 02 Sep 2009
Posts: 57025
If |x – 6| = 5, what is the value of x?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 65% (00:56) correct 35% (01:02) wrong based on 141 sessions

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

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

_________________
VP  D
Joined: 05 Mar 2015
Posts: 1007
Re: If |x – 6| = 5, what is the value of x?  [#permalink]

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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
Manager  B
Joined: 02 Nov 2013
Posts: 79
Location: India
Re: If |x – 6| = 5, what is the value of x?  [#permalink]

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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.

Answer B.
Intern  B
Joined: 04 Sep 2017
Posts: 18
Re: If |x – 6| = 5, what is the value of x?  [#permalink]

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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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Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3605
Re: If |x – 6| = 5, what is the value of x?  [#permalink]

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

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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  B
Joined: 09 May 2015
Posts: 5
Re: If |x – 6| = 5, what is the value of x?  [#permalink]

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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.
can someone please help where am i going wrong?
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If |x – 6| = 5, what is the value of x?  [#permalink]

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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.
can someone please help where am i going wrong?

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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If |x – 6| = 5, what is the value of x?  [#permalink]

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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.

Therefore, B is the answer.
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Re: If |x – 6| = 5, what is the value of x?  [#permalink]

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_________________ Re: If |x – 6| = 5, what is the value of x?   [#permalink] 08 Aug 2019, 12:47
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