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If |x+1/2|=|y+1/2|, what is the value of x+y?

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by Max@Math Revolution » Tue Mar 20, 2018 12:40 am
[GMAT math practice question]

If |x+1/2|=|y+1/2|, what is the value of x+y?

1) xy<0
2) x>0 and y<0
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Source: — Data Sufficiency |
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by GMATGuruNY » Tue Mar 20, 2018 1:39 am
Max@Math Revolution wrote:[GMAT math practice question]

If |x+1/2|=|y+1/2|, what is the value of x+y?

1) xy<0
2) x>0 and y<0
Case 1: Signs unchanged
x + 1/2 = y + 1/2
x = y.

Case 2: Signs changed in ONE of the absolute values
x + 1/2 = -y - 1/2
x+y = -1

Question stem, rephrased:
If x = y or x+y = -1, what is the value of x+y?

Statement 1: xy<0
Since x≠y, x+y = -1.
SUFFICIENT.

Statement 2: x>0 and y<0
Since x≠y, x+y = -1.
SUFFICIENT.

The correct answer is D.
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by Max@Math Revolution » Wed Mar 21, 2018 11:44 pm
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

|x+1/2|=|y+1/2|
=> |x+1/2|^2=|y+1/2|^2
=> (x+1/2)^2=(y+1/2)^2
=> x^2 + x + 1/4 = y^2 + y + 1/4
=> x^2 - y^2 + x - y = 0
=> (x-y)(x+y)+(x-y) = 0
=> (x-y)(x+y+1) = 0
=> x=y or x+y=-1

Condition 1)
Since xy < 0, we have x≠y and x+y = -1 from the original condition.

Condition 2)
Since x > 0 and y < 0, we have x≠y and x+y = -1 from the original condition.

Therefore, D is the answer.

By Tip 1), D is most likely to be the answer.

Answer: D
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