If x and y are integers and \(x=\frac{y}{5}+2\)  , is xy even?

Question: If x and y are integers and \(x=\frac{y}{5}+2\), is xy even?

1. 5x – 10 is even
2. \(\frac{y}{x}\)is even

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.

“If x and y are integers and \(x=\frac{y}{5}+2\), is xy even?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

As x and y are integers then xy will be even if atleast one of the multiple is even.

From the expression given in the question: \(x=\frac{y}{5}+2\) , we have that y = 5x – 10

Taking statement (1), we have: 5x – 10 is even.

Since y = 5x – 10 then y = 5x – 10 = even

Hence this statement is sufficient.

Taking statement (2), we have: \(\frac{y}{x}\) = even

So, y = x * even = even

Hence this statement is sufficient.

Correct option: D

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