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# What is the value of |x - 2|?

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What is the value of |x - 2|?  [#permalink]

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Updated on: 29 Oct 2015, 05:32
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What is the value of |x - 2|?

(1) |x - 4| = 2

(2) |2 - x| = 4

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Originally posted by sony1000 on 29 Oct 2015, 05:15.
Last edited by Bunuel on 29 Oct 2015, 05:32, edited 1 time in total.
Edited the question and added the OA.
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Re: What is the value of |x - 2|?  [#permalink]

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29 Oct 2015, 05:48
2
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sony1000 wrote:
What is the value of |x - 2|?

(1) |x - 4| = 2

(2) |2 - x| = 4

(1) says that the distance between x and 4 is 2, which means that x can be 2 or 6. If x is 2, then the distance between 2 and 2 is 0 but if x is 6, then the distance between 6 and 2 is 4. Not sufficient.

(2) directly tells that the distance between 2 and x is 2. Sufficient.

Hope it's clear.
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Re: What is the value of |x - 2|?  [#permalink]

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30 Oct 2015, 14:05
2
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Hi sony1000,

When an absolute value 'sign' shows up in a Quant question, you're often being tested on the 'thoroughness' of your thinking (so be on the lookout for more than just the obvious possibilities...

In this prompt, we're asked for the value of |X - 2|.

1) |X - 4| = 2

The obvious solution to this equation is X = 6 (since 6 - 4 = 2), but is that the ONLY answer? Remember that an absolute value 'turns' a negative result into a positive one. Thus X = 2 is ALSO a solution (since 2 - 4 = -2 and |-2| = 2).

IF...
X = 6 then the answer to the question is |6-2| = |4| = 4

IF...
X = 2 then the answer to the question is |2-2| = |0| = 0
Fact 1 is INSUFFICIENT

2) |2 - X| = 4

The same logic applies to this equation - there are likely 2 solutions...

Those two solutions are X = -2 (since 2 - -2 = 4) and X = 6 (since 2 - 6 = -4 and |-4| = 4).

IF...
X = 6 then the answer to the question is |6-2| = |4| = 4

IF...
X = -2 then the answer to the question is |-2-2| = |-4| = 4
The solution remains the SAME regardless of which value of X you use.
Fact 2 is SUFFICIENT

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Re: What is the value of |x−2|?  [#permalink]

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10 Oct 2016, 08:27
Bunuel wrote:
What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4

Stat 1: Left and right side are positive ...so square them

(x-4)^2 = 4 => x^2 - 8x + 16 = 4 => x^2 - 8x +12 = 0 ...x = 2 and 6...two values..Insufficient.

Stat 2: 4 + x^2 - 8x = 4 => x^2 - 8x = 0 => x = 8...Sufficient.

IMO option B.
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What is the value of |x−2|?  [#permalink]

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10 Oct 2016, 09:49
1
msk0657 wrote:
Bunuel wrote:
What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4

Stat 1: Left and right side are positive ...so square them

(x-4)^2 = 4 => x^2 - 8x + 16 = 4 => x^2 - 8x +12 = 0 ...x = 2 and 6...two values..Insufficient.

Stat 2: 4 + x^2 - 8x = 4 => x^2 - 8x = 0 => x = 8...Sufficient.

IMO option B.

You forgot to Square the RHS of the highlighted equation above. Please check again.

Here is how I solved :

Statement 1 : |x-4|=2

Either x-4 =2 => x=6
or 4-x = 2 => x =2 Hence, insufficient.

Statement 2 : |2-x|=4

Either 2-x = 4 or x = -2
or x-2 = 4 or x = 6.

For both x = -2 and x = 6, we will get the distinct value of |x-2|. Hence, Sufficient.
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Re: What is the value of |x−2|?  [#permalink]

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10 Oct 2016, 10:10
1
abhimahna wrote:
msk0657 wrote:
Bunuel wrote:
What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4

Stat 1: Left and right side are positive ...so square them

(x-4)^2 = 4 => x^2 - 8x + 16 = 4 => x^2 - 8x +12 = 0 ...x = 2 and 6...two values..Insufficient.

Stat 2: 4 + x^2 - 8x = 4 => x^2 - 8x = 0 => x = 8...Sufficient.

IMO option B.

You forgot to Square the RHS of the highlighted equation above. That's the reason you got B sufficient. Please check again.

Here is how I solved :

Statement 1 : |x-4|=2

Either x-4 =2 => x=6
or 4-x = 2 => x =2 Hence, insufficient.

Statement 2 : |2-x|=4

Either 2-x = 4 or x = -2
or x-2 = 4 or x = 6, Hence, insufficient.

Combining, x = 6. hence, Sufficient.

I believe answer should B and not C. Check both the solutions that you get from statement 2, we get 4 in both cases-so B is sufficient.
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Re: What is the value of |x−2|?  [#permalink]

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10 Oct 2016, 10:19
KS15 wrote:
I believe answer should B and not C. Check both the solutions that you get from statement 2, we get 4 in both cases-so B is sufficient.

ohh yeahh, you are right. I missed that point. Thanks.

That means I should now stop doing questions for the day. My brain seems tired now after a lot many questions done in the day
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What is the value of |x−2|?  [#permalink]

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10 Oct 2016, 10:32
1
Bunuel wrote:
What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4

B

Law of multiplicativeness says:

|ab|=|a||b|

Implies,
|x-2| = |(-1)(2-x)| = |-1|*|2-x| = |2-x|

From statement 2 -> |2-x| = 4

Therefore, statement 2 is sufficient.

Statement 1, gives x = 2 and 6
or, x-2 = 0 or 4.

Therefore, statement 1 is not sufficient.

Hence, B
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Re: What is the value of |x−2|?  [#permalink]

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16 Oct 2016, 20:03
Bunuel wrote:
What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4

B

Law of multiplicativeness says:

|ab|=|a||b|

Implies,
|x-2| = |(-1)(2-x)| = |-1|*|2-x| = |2-x|

From statement 2 -> |2-x| = 4

Therefore, statement 2 is sufficient.

Statement 1, gives x = 2 and 6
or, x-2 = 0 or 4.

Therefore, statement 1 is not sufficient.

Hence, B

Here x gives -2 and 6 not 2 and 6.

Hence, both value suffices, the equation, hence it should be C.

PS: If any value doesnt suffice the equation, then there has been calculation problem.
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What is the value of |x−2|?  [#permalink]

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16 Oct 2016, 20:37
rahul202 wrote:
Bunuel wrote:
What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4

B

Law of multiplicativeness says:

|ab|=|a||b|

Implies,
|x-2| = |(-1)(2-x)| = |-1|*|2-x| = |2-x|

From statement 2 -> |2-x| = 4

Therefore, statement 2 is sufficient.

Statement 1, gives x = 2 and 6
or, x-2 = 0 or 4.

Therefore, statement 1 is not sufficient.

Hence, B

Here x gives -2 and 6 not 2 and 6.

Hence, both value suffices, the equation, hence it should be C.

PS: If any value doesnt suffice the equation, then there has been calculation problem.

Hi,

The ans is B only, and I did not quite understand what you are trying to tell me.

Maybe the reason for the confusion is that I did not explicitly mention what I meant by statement 1.
By statement 1, I meant |x−4|=2
The above statement is true for x = 2 and 6 only!

B is the solution to the above question because both the values of x that satisfies the equation |2−x|=4, give the same and one unique value of the equation |x−2| i.e. 4.
Hence B.

My intention of writing a new answer was to point out that in this case, we do not even need to solve statement 2 to get values of x that satisfies it. Hence, the examinee can save some time there.

Thanks,
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What is the value of |x−2|?  [#permalink]

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12 Jan 2017, 06:11
Bunuel wrote:
What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4

B

Law of multiplicativeness says:

|ab|=|a||b|

Implies,
|x-2| = |(-1)(2-x)| = |-1|*|2-x| = |2-x|

From statement 2 -> |2-x| = 4

Therefore, statement 2 is sufficient.

Statement 1, gives x = 2 and 6
or, x-2 = 0 or 4.

Therefore, statement 1 is not sufficient.

Hence, B

Since, |A|=B can be written as A= ±B.
So, in statement II: |2−x|=4 -->2-x= ±4, now multiplying -1 on both sides we get x-2=±4 (±4 multiplied to -1 will result ±4 only!).
Therefore, x-2=±4-->|x−2|=4.
But, performing above operation for statement I will give different results for |x−2|.

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Re: What is the value of |x - 2|?  [#permalink]

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13 Apr 2017, 03:44
Quite easy question.
(1) - The equation |x-4|=2 tells you that X=6 or X=2
|x-2|=4 or |x-2|=0
Insufficient
(2) - No need to solve the equation since you know that |x|=|-x|
|x-2|=|2-X|=4
Sufficient

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Re: What is the value of |x - 2|?  [#permalink]

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13 Apr 2017, 12:28
What is the value of |x - 2|?

Question asks what is the distance of 2 from x ?

(1) |x - 4| = 2

This statement gives the distance of 4 from x.

Now x can be towards the right of 4

2--4--x

In this case distance of 2 from x becomes 4

Now x can be towards the left of 4

2--x--4

In this case distance of x from 2 becomes 0.

As we have two different scenarios, this statement is insufficient.

(2) |2 - x| = 4

can be written as |-(x-2)| = 4

can be further written as |(x-2)| = 4

Hence this gives us what we are looking for. The distance of 2 from x = 4

This statement is sufficient

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Re: What is the value of |x - 2|?  [#permalink]

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23 Apr 2017, 10:37
Bunuel wrote:
sony1000 wrote:
What is the value of |x - 2|?

(1) |x - 4| = 2

(2) |2 - x| = 4

(1) says that the distance between x and 4 is 2, which means that x can be 2 or 6. If x is 2, then the distance between 2 and 2 is 0 but if x is 6, then the distance between 6 and 2 is 4. Not sufficient.

(2) directly tells that the distance between 2 and x is 2. Sufficient.

Hope it's clear.

Hi Bunuel ,

Thanks for sharing the solution.

With reference to statement 2 , does it mean that |x-2| and |2-x| refer to same thing and in both cases distance will be same?
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Re: What is the value of |x - 2|?  [#permalink]

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23 Apr 2017, 22:38
2201neha wrote:
Bunuel wrote:
sony1000 wrote:
What is the value of |x - 2|?

(1) |x - 4| = 2

(2) |2 - x| = 4

(1) says that the distance between x and 4 is 2, which means that x can be 2 or 6. If x is 2, then the distance between 2 and 2 is 0 but if x is 6, then the distance between 6 and 2 is 4. Not sufficient.

(2) directly tells that the distance between 2 and x is 2. Sufficient.

Hope it's clear.

Hi Bunuel ,

Thanks for sharing the solution.

With reference to statement 2 , does it mean that |x-2| and |2-x| refer to same thing and in both cases distance will be same?

Yes. Generally |a - b| = |b - a|.
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Re: What is the value of |x - 2|?  [#permalink]

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01 Sep 2017, 19:07
sony1000 wrote:
What is the value of |x - 2|?

(1) |x - 4| = 2

(2) |2 - x| = 4

Stmnt 1

x -4 = 2
x =6

-lx-4l =2
-x +4 =2
x=2

Insuff

Stmnt 2

2 - x = 4
x= 2

-l2 - x| = 4
-2 + x =4
x =6

Suff

B
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Re: What is the value of |x - 2|?  [#permalink]

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16 Feb 2019, 20:49
sony1000 wrote:
What is the value of |x - 2|?

(1) |x - 4| = 2

(2) |2 - x| = 4

Even after getting 2 critical point, its a good thing to check if those values satisfy the mod or not

Lets start now

So for 1, we get the point as x = 4

Now there can be 2 cases, x < 4 & x > 4

When we solve the mod using those 2 inequalities, we get x =-6 and x = 6, when put back in the statement, gives us 2 values
10 =! 2 & 2=2

From 2) |2 - x| = 4, we get the regions as x<2 & x > 2

When we solve the mod using those 2 inequalities, we get x =-2 and x = 6, when put back in the statement, gives us 2 equal values

Sufficient
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Re: What is the value of |x - 2|?   [#permalink] 16 Feb 2019, 20:49
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