# GMAT DS : Number Theory

Number Theory is a big hit with the GMAT test setters, especially when setting Data Sufficiency Questions.

Here is a GMAT DS practice question from the Number Theory topic.

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.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Question
When Y is divided by 2, is the remainder 1?
1. (-1)(Y+2) = -1
2. Y is prime

The given question is an "Is" question. "IS" questions have to answered with an unswerving YES or NO. If your answer to this question is SOMETIMES YES and SOMETIMES NO or in other words MAYBE, then you have not answered the question.

Let us evaluate statement 1.

(-1)(Y+2) = -1.
(-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.

Statement 1 is sufficient.
The answer is either choice (A) or choice (D).

Now let us evaluate the statement 2.

Y is prime

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

All other prime numbers are odd numbers.
So, when Y is divided by 2, the remainder is '1'.

We cannot conclude is Y is 2 or other prime numbers.

As we are not able to conclude if Y is an even number or an odd number with statement 2, it is not sufficient.

Hence, answer is choice (A ).