GMAT Question Bank | Number Properties DS Q29

This GMAT math practice question is a data sufficiency question from Number Properties and Number Systems. Concept: Odd and even numbers, positive and negative numbers, prime and composite numbers. Level of difficulty: GMAT 600 level question. Easy question.

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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.
4. EACH 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 29: When the positive integer Y is divided by 2, is the remainder 1?

1. (-1)^{(Y + 2)} = -1
2. Y is prime

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Video Explanation

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Explanatory Answer

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" questions 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.

What additional information do we have about Y from the question stem?
'Y' is a positive integer.

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Step 2 of solving this GMAT DS question:
Evaluate Statement (1) ALONE: (-1)^(Y+2) = -1

Property: (-1)^{ODD NUMBER} = -1

Therefore, Y + 2 is an odd number.
Hence, Y has to be an odd number.
So, when Y is divided by 2, the remainder is 1.
The answer to the question is a definite YES.

Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.

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Step 3 of solving this GMAT DS question:
Evaluate Statement (2) ALONE: Y is prime.

Possibility 1: Y could be '2' which is an even number.
So, if Y is 2, when Y is divided by 2, the remainder is '0'.

Possibility 2: Any prime number other than 2
All prime numbers other than 2 are odd numbers.
So, if Y is one of the other prime numbers, when Y is divided by 2, the remainder is '1'.
We donot have enough data in the question stem or statement 2 to conclude whether Y is 2 or one of the other prime numbers.
As we are not able to conclude whether Y is an even number using statement 2, it is not sufficient.

Statement 2 ALONE is NOT sufficient.
Eliminate choice D.

Statement 1 ALONE is sufficient, but statement 2 is not sufficient. Choice A is the answer.