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Data Sufficiency - August 17, 2004
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 July or the meaning of counterclockwise), you must indicate whether
| A. |
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. |
| B. |
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. |
| C. |
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. |
| D. |
EACH statement ALONE is sufficient to answer the question asked. |
| E. |
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. |
Note
In data sufficient problems that ask for the value of a quantity the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.
Question
Is y an integer?
A. y3 is an integer
B. 3y is an integer
The correct choice is (C). Answer (BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NIETHER statement ALONE is sufficient.)
Explanatory Answer
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.
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.
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 best answer.
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