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Data Sufficiency - Number Theory - April 18, 2005
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
What is the value of X, if X and Y are two distinct integers and their product is 30?
1. X is an odd integer
2. X > Y
The correct choice is (E). The correct answer is (The value of X cannot be determined from the information provided)
Explanatory Answer
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 manner
| 1 * 30 |
|
(-1) * (-30) |
| 2 * 15 |
|
(-2) * (-15) |
| 3 * 10 |
|
(-3) * (-10) |
| 5 * 6 |
|
(-5) * (-6) |
Statement 1: 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 the information in statement I we will not be able to conclusively decide the value of X. Hence, statement I alone is not sufficient to answer the question.
Statement 2: From this statement, we know that the value of X > Y. From the given combinations, X can take more than one value. Hence, using the information in statement II, we will not be able to find the value of X.
Combining the two statements, we know that X is odd and that the value of X > Y.
The combinations that satisfy both the conditions include X taking the value of -1, -3 and -5.
As the information provided in the two statements independently or together are not sufficient to answer the question, the answer choice is (E).
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