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Data Sufficiency - March 30, 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 a leap year or the meaning of the word 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. |
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.
Question
Is m divisible by 6?
(1) m is divisible by 3
(2) m is divisible by 4
The correct choice is (C).
Explanatory Answer
We need to answer if m is divisible by 6. The answer has to be a definitive YES or a NO.
The test of divisibility for 6 is that the number should be divisible by both 3 and 2.
From statement (1) we know that m is divisible by 3. However, this does not answer the question if m is also divisible by 2. Hence, statement (1) alone is not sufficient. We can rule out answer choices (A) and (D). The correct answer has to be one of the other three viz., (B), (C) or (E).
From statement (2) we know that m is divisibly by 4. If m is divisible by 4, then m should surely be divisible by 2. However, from statement (2) alone we do not know if m is divisible by 3. Therefore, statement (2) alone is also not sufficient. Hence, we can eliminate answer choice (B).
Combining the two statements, we know that m is divisible by 3 and by 4. Hence, we can conclude that m is divisible by 6. Choice (C ) is correct.
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