## Arithmetic Concepts in GMAT Quant

# Properties of integers questions involving multiples

There are many GMAT Quant questions testing you on the properties of integers. In addition, there are many properties of integers you must know to answer these questions efficiently. Reviewing these properties of integers is a good idea.

Consider the following data sufficiency question from GMAT Tutor:

*If m and k are non-zero integers, is m a multiple of k?(1) (m ^{2}+m)/k is an integer.(2) m=2k^{2}−3k*

## How to solve it

As with many data sufficiency questions, one statement seems easier to deal with than the other. In this case it is easier to assess Statement (1).

Simply plug in numbers to assess Statement (1).

- Imagine k is 2.
- A larger even number divided by 2 will always bring you to an integer, so imagine m is 4.
- (4
^{2}+4)/2 = 10, complying with Statement (1). - So, m is a multiple of k.

However, imagine k is 2 and m is 3.

- (3
^{2}+3)/2 = 6, again complying with Statement (1). - However, in this case, m is not a multiple of k.
- Therefore, Statement (1) is not sufficient. Eliminate A & D as possible answer choices.

Consider Statement (2).

- Look at 2k
^{2}−3k. - We don’t need to plug in numbers here. We see that 2k
^{2}is a multiple of k. Also, 3k is also a multiple of k. A multiple of k subtracted from a multiple of k will always lead to a multiple of k. - Thus, m is a multiple of k.
- Statement (2) is sufficient alone, and thus, the correct answer choice is B.

## An important point to remember

Therefore, the rule you should remember from this questions is that a multiple of x – a multiple of x = a multiple of x.

When using questions for preparation, you are always searching for the things you can take from the questions and apply on test day. This is an example in which we used multiple strategies to arrive at the correct answer.