What is the value of X, if X and Y are two distinct integers and their...
Step 1: Understand the Question Stem
What kind of an answer will the question fetch?
The question is a "What is the value?" question. The answer has to be a value, a number for 'X'.
When is the data sufficient?
The data is sufficient if we are able to get a UNIQUE answer for the value of 'X' from the information in the statements.
Do we have any additional information about 'X' or 'Y' from the question stem?
From the question, we know that both X and Y are distinct integers and their product is 30.
30 can be obtained as a product of two distinct integers in the following ways.
Values that satisfy X × Y = 30
Step 2: Evaluate Statement (1) ALONE: X is an odd integer
From this statement, we know that the value of X is odd.
Therefore, X can be one of the following values: 1, -1, 3, -3, 5, -5.
So, using information in statement 1 we will not be able to deduce a UNIQUE value for X.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Step 3: Evaluate Statement (2) ALONE: X > Y
From this statement, we know that the value of X > Y.
From the combinations listed in the table above, X can take more than one value. Here are two possibilities: X could be 10 and Y could be 3. Or X could be 30 and Y could be 1.
Hence, using information in statement 2, we will not be able to find a UNIQUE value for X.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Step 4: Evaluate Statements (1) & (2) Together: X is an odd integer and X > Y
Values of X and Y that satisfy both the conditions are
More than one value exists for X. Because we are not able to deduce a UNIQUE value for X using information provided in the two statements together, the given data is NOT sufficient.
Statements TOGETHER are NOT SUFFICIENT. Choice E is the answer.