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The question basically asks about the distance between x and 2.
(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.
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
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.
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|.
Hence, B is answer.
_________________
--Asis
1.01^365= 37.8, but 0.99^365=0.03. Give a extra step each day to take big results!!
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
Answer is B
_________________
What was previously considered impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them
The question basically asks about the distance between x and 2.
(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.
Answer: B.
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?
The question basically asks about the distance between x and 2.
(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.
Answer: B.
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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46% (01:16) correct 
