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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the value of x? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## What is the value of x? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] What is the value of x? 1) |x+y| = |x-y| 2) |y| > y _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

What is the value of x?

1) |x+y| = |x-y|
2) |y| > y
Statement 1:
Squaring both sides, we get:
xÂ² + yÂ² + 2xy = xÂ² + yÂ² - 2xy
4xy = 0
xy = 0
Case 1: x=0, with the result that y can be any value
Case 2: y=0, with the result that x can be any value
Since Case 2 allows x to be any value, INSUFFICIENT.

Statement 2:
Here, y can be any negative value.
INSUFFICIENT.

Statements combined:
Since Statement 2 requires that y < 0, only Case 1 satisfies both statements.
In Case 1, x=0.
SUFFICIENT.

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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.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

|x+y|=|x-y|
=> |x+y|^2=|x-y|^2
=> (x+y)^2=(x-y)^2
=> x^2+2xy+y^2=x^2-2xy+y^2
=> 4xy = 0
=> xy = 0
=> x = 0 or y = 0
Condition 1) is equivalent to x = 0 or y = 0. Condition 1) is not sufficient.
Condition 2) is equivalent to y < 0. It follows from condition 2) that x = 0 since y canâ€™t be zero.
Both conditions 1) & 2) together are sufficient since they yield a unique solution.

Since this question is an absolute value question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

However, as we have seen above, neither condition 1) nor condition 2) is sufficient on its own.

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