GMAT Data Sufficiency - Is |x-10| > |x-30|

Question: Is |x-10| > |x-30|

(1) x>10
(2) x>25

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.        
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.        
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.        
4. EACH statement ALONE is sufficient.        
5. Statements (1) and (2) TOGETHER are not sufficient.

“Is |x-10| > |x-30|” is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Quantitative Review 2017". GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. This particular GMAT data sufficiency question assesses candidates’ critical thinking and hypervigilance. An abstract problem-solving question is mainly given and most of the difficulty comes from obtuse or clever wording, candidates usually miss it.

Solution and Explanation:

Approach Solution 1:

Explanation: This is a data sufficiency question that provides a given situation where Is |x-10| > |x-30| 
In order to prove that it is true, there are two statements that have been identified which need to be proved to be sufficient in relevance to the case. 
Accordingly, 
|a - b| always means "the distance between a and b on the number line". So the inequality
|x - 10| > |x - 30| is the given case. 
It means in words that "the distance between x and 10 is greater than the distance between x and 30". In other words, it can be evaluated that "x is closer to 30 than it is to 10". 
However, for that to be true, x needs to be greater than the midpoint of 10 and 30, so x needs to be greater than 20.
The first given data states that x > 10 which clearly implicates that this is not sufficient as x needs to be more than 20. 
However, the second condition identifies x > 25 which is basically the required value thereby statement 2 being sufficient only. 

Approach Solution 2:

Explanation: In the given case of this data sufficient question is based on whether |x-10| > |x-30|. Accordingly, two conditions have been given to identify whether the data is sufficient to prove the case. 
In order to solve this problem, the mathematical approach can also be used to evaluate. This equals as follows: 
|x-10| > |x-30|
Squaring both sides, the equation would result in- 
(x-10)^2 > (x-30)^2
(x^2+100-20x)>(x^2+900-60x)
(60x-20x)>(900-100)
40x>800
x>20
Thus, it can be concluded that for the given |x-10| > |x-30| to be true, x needs to be greater than 20 which states that only statement 2 is correct and sufficient.

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