Question: If y is an odd number and x^3 ∗ y^4 = 648, y=?

1) y is positive.
2) x is an integer.

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 y is an odd number and x^3 ∗ y^4 = 648, y=? 1) y is positive. 2) x is” is a topic of the GMAT Quantitative reasoning section of GMAT. The questions of GMAT Data Sufficiency constitute a problem statement along with two factual statements. This specific GMAT data sufficiency assesses the candidate’s proficiency to assert mathematically. It enables the candidates to solve quantitive problems in a logical way with mathematical evidence. The difficult aspect of these questions lies in their wording which candidates usually miss. The GMAT Quant section includes 31 questions as a whole. The GMAT data sufficiency portion contains 15 questions which are mostly two-fifths of the entire 31 GMAT quant questions.

Solution and Explanation:

There is only one solution to this problem.

Approach Solution 1:

The problem statement informs that:

Given:

• y is an odd number
• x^3 ∗ y^4 = 648

Find out:

• The value of y.

Since, x^3 ∗ y^4 = 648, then we can derive the number 648 as 2^3 * 3^4. Then it can be inferred that x=2 and y=3

1. The statement states that y is positive. There is nowhere mentioned that y is an integer. Then it is not possible for us to know the value of y.
   Therefore, the statement alone is not sufficient to find the value of y.
2. The statement indicates that x is an integer. Then we can assume the value of y is positive or negative since the power of y is 4. Therefore, the statement alone is insufficient to find the value of y.
   By combining both statements, we get,
   x is an integer and y is positive.
   Then it can be confirmed that the value of y is an integer and y= 3 is relevant since it is an odd number.
   Therefore, both statements together are sufficient to find the value of y.

Correct Answer: (C)

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