Step 1 of solving this GMAT DS question: Understand the Question Stem
What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" question is either YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
If the answer is MAYBE or DONOT KNOW, the data is NOT sufficient.
Do we have any more information about x and y from the question stem?
The question stem states that both x and y are positive integers.
Step 2 of solving this GMAT DS question: Evaluate Statement (1) ALONE
Statement (1) : x is odd.
The statement provides no information about y.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
Step 3 of solving this GMAT DS question: Evaluate Statement (2) ALONE
Statement (2) : xy is odd.
Given that x and y are integers and that the product xy is odd, both x and y have to be odd (product of two odd integers is odd).
We can answer the question with a definite YES.
Eliminate choices C and E.
Statement 2 ALONE is sufficient. Choice B is the answer.
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