# GMAT Quant Question Bank | Number Systems Q12

#### GMAT Data Sufficiency Practice | Properties of odd and even numbers

This GMAT DS question is a Number Systems & Number Properties question testing concepts in properties of odd and even numbers. An easy GMAT sub 600 level data sufficiency sample 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 -

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
5. 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 12: If x and y are positive integers, is y odd?

1. x is odd.
2. xy is odd.

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#### Step 1 of solving this GMAT DS question: Understand the Question Stem

What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" question is either YES or NO.

When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
If the answer is MAYBE or DONOT KNOW, the data is NOT sufficient.

The question stem states that both x and y are positive integers.

#### Step 2 of solving this GMAT DS question: Evaluate Statement (1) ALONE Statement (1) : x is odd.

The statement provides no information about y.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.

#### Step 3 of solving this GMAT DS question: Evaluate Statement (2) ALONE Statement (2) : xy is odd.

Given that x and y are integers and that the product xy is odd, both x and y have to be odd (product of two odd integers is odd).
We can answer the question with a definite YES.

Eliminate choices C and E.

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