Data Sufficiency

[GMAT math practice question]

What is the value of x?

1) |x+y| = |x-y|
2) |y| > y

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:
x² + y² + 2xy = x² + y² - 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.
No information about x.
INSUFFICIENT.

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

The correct answer is C.

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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 can'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.

Therefore, C is the answer.
Answer: C