The given question is a data sufficiency question in number properties and tests concepts in number of factors of a number and properties of odd and even integers. It is a medium difficulty GMAT 650 level DS question.

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 -

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

All numbers used are real numbers.

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.

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 25: What is the value of X, if X and Y are two distinct integers and their product is 30?

- X is an odd integer
- X > Y

**What kind of an answer will the question fetch?**

The question is a "What is the value?" question. The answer has to be a value, a number for 'X'.

**When is the data sufficient?**

The data is sufficient if we are able to get a UNIQUE answer for the value of 'X' from the information in the statements.

**Do we have any additional information about 'X' or 'Y' from the question stem?**

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 ways.

S No. | Positive X and Y | Negative X and Y |
---|---|---|

1 | 1 × 30 | (-1) × (-30) |

2 | 2 × 15 | (-2) × (-15) |

3 | 3 × 10 | (-3) × (-10)) |

4 | 5 × 6 | (-5) × (-6) |

Evaluate Statement (1) ALONE: X is an odd integer

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 information in statement 1 we will not be able to deduce a UNIQUE value for X.

**Statement 1 ALONE is NOT sufficient.**

Eliminate choices A and D. Choices narrow down to B, C, or E.

Evaluate Statement (2) ALONE: X > Y

From this statement, we know that the value of X > Y.

From the combinations listed in the table above, X can take more than one value. Here are two possibilities: X could be 10 and Y could be 3. Or X could be 30 and Y could be 1.

Hence, using information in statement 2, we will not be able to find a UNIQUE value for X.

**Statement 2 ALONE is NOT sufficient.**

Eliminate choice B. Choices narrow down to C or E.

Evaluate Statements (1) & (2) Together: X is an odd integer and X > Y

Values of X and Y that satisfy both the conditions are

S No. | X is odd and X > Y |
---|---|

1 | (-1) × (-30) |

2 | (-3) × (-10)) |

3 | (-5) × (-6) |

More than one value exists for X. Because we are not able to deduce a UNIQUE value for X using information provided in the two statements together, the given data is NOT sufficient.

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