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### Data Sufficiency (DS) - Quant/Math - CAT 2016

Question 4 the day: April 18, 2005

The question for the day is a data sufficiency question.

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 -

Choose 1 if the question can be answered by one of the statements alone and not by the other.
Choose 2 if the question can be answered by using either statement alone
Choose 3 if the question can be answered by using both the statements together, but cannot be answered by using either statement alone
Choose 4 if the question cannot be answered even by using both statements together

Question:
What is the value of X, if X and Y are two distinct integers and their product is 30?
I. X is an odd integer
II. X > Y
Correct choice (4). Correct Answer - (The value of X cannot be determined from the information provided)

Solution:

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 I: 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 II: 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 (4).

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