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Directions

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4. EACH statement ALONE is sufficient to answer the question asked.
5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Numbers
All numbers used are real numbers.

Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

Note
In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Is y an integer?

(1) y³ is an integer
(2) 3y is an integer

The correct choice is (C). Answer BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient.

From statement (1), we know that y³ is an integer.

However, that does not necessarily mean that y is an integer.

Let us say, y³ = 2, then y is not an integer. However, if y³ = 8, then y = 2 and is an integer. So, statement A alone is not sufficient.

Hence, we can eliminate answer choices (A) and (D).

From statement (2), we know that 3y is an integer.

However, that does not necessarily mean that y is an integer.

Let us say 3y = 2, then y is not an integer.

However, if 3y = 3, then y will be an integer.

Hence, statement (2) is also not sufficient.

We can eliminate answer choice (B)

When we combine the two statements, we get that y³ is an integer and 3y is also an integer.

Only for integer values of y, will both y³ and 3y simultaneously be integers.

As both the statements together are needed to answer the question, choice (C) is the correct answer.