# GMAT Tip: Tackling Remainder Questions

*The GMAT Tip of the Week is a weekly column that includes advice on taking the Graduate Management Admission Test, which is required for admission to most business schools. Every week an instructor from a top test-prep company will share suggestions for improving your GMAT score. This week’s tip comes from Brent Hanneson, creator of GMAT Prep Now, a Web site offering on-demand videos that teach GMAT skills.*

Consider the following question:

N is a positive integer. When N is divided by 13, the remainder is 5. When N is divided by 46, the remainder is 31. What is the smallest possible value of N?

Before we examine the solution to this question, I’d like to ask an easier question:

N is a positive integer. When N is divided by 7, the remainder is 3. What are three possible values of N?

Does your list include 3 as a possible value for N? It should since 3 is the smallest number that meets the given criteria (3 divided by 7 equals 0 with a remainder of 3).

When it comes to GMAT questions involving remainders, it’s often useful to begin listing numbers that meet the given criteria. When it comes to listing possible values, we have a useful rule:

If N and D are positive integers, and if N divided by D is equal to Q with remainder R, then the possible values of N are: R, R+D, R+2D, R+3D,. . .

Example: When positive integer W is divided by 6, the remainder is 5. Given this information, the possible values of W are: 5, 5+6, 5+2(6), 5+3(6), 5+4(6), . . .

Upon simplification, we find that the possible values of W are: 5, 11, 17, 23, 29 and so on.

The important takeaway is that you can sometimes save yourself a lot of work by listing possible values and, more importantly, by including the smallest possible value in that list.

Now back to the original question:

N is a positive integer. When N is divided by 13, the remainder is 5. When N is divided by 46, the remainder is 31. What is the smallest possible value of N?

First, if N divided by 13 gives us a remainder of 5, the possible values of N are: 5, 18, 31, 44, 57 and so on.

Second, if N is divided by 46 gives us remainder 31, the possible values of N are: 31, … STOP.

Since both lists include 31, the answer to our original question must be 31.

So, when you encounter a GMAT remainder question, one approach may involve identifying possible values of a certain number. When identifying those values, it may be to your advantage to identify the smallest possible value.

*Brent Hanneson, the creator of GMAT Prep Now, has worked in the field of education for most of his career. He has taught courses at three different test-prep companies and created comprehensive GMAT and GRE courseware packages used by the University of British Columbia and 12 other universities across North America.*

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