If x is an integer, is √(3x - y) = √(2x – 2y)? (1) x – y = 2 (2) x +

The answer should be Option B for the given question. I typed A instead of B earlier. have made correction

What is the OE? I think the answer should be C. Bunuel can you help.?

Ho ahead and post your solution please.

The OA is B. GMATinsight's solution above is spot on.

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

The question asks if \(x + y = 0\).

\(\sqrt{3x-y} = \sqrt{2x-2y}\)
\(⇔ 3x-y = 2x - 2y\)
\(⇔ x + y = 0\)

Since condition 2) "\(x+y=4\)" tells the answer is 'no' and 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.

Condition 1)
If \(x = 1\) and \(y = -1\), then we have \(x + y = 0\) and the answer is 'yes'.
If \(x = 2\) and \(y = 0\), then we have \(x + y = 2\) and the answer is 'no'.

Since condition 1) does not yield a unique solution, it is not sufficient

Therefore, B is the answer.

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