Source: Official Guide for GMAT Review 2016 Problem Solving; #106

1

# If n is an integer greater than

If n is an integer greater than 6, which of the following must be divisible by 3?

### 2 Explanations

1 Cydney Seigerman, Magoosh Tutor

Hi Sneha :)

Great question! Yes, in the problem, the phrase "integers greater than 6" does all integers (2-digit numbers, 3-digit numbers, etc.) that are larger than 6. However, we can classify all of these integers into three different cases based on their remainder when divided by 3:

Case 1: Integers that have a remainder of 2 when divided by 3.
Case 2: Integers that have a remainder of 1 when divided by 3.
Case 3: Integers that have a remainder of 0 when divided by 3.

Each of the three numbers used in the explanation video reflect one of the cases:

Case 1: 8 --> 8/3 = 2r2
Case 2: 7 --> 7/3 = 2r1
Case 3: 9 --> 9/3 = 3r0

All other integers greater than 6 will fall into one of these cases and will therefore exhibit the same divisibility characteristics of their 1-digit counterparts. So we can limit our discussion in this problem to the three numbers listed above, simplifying the problem and allowing us to determine the correction solution faster :)

I hope this helps!

Nov 21, 2015 • Comment

1 Catherine Guivencan, Magoosh Tutor

Aug 14, 2015 • Comment

Sneha Kalaivanan

Wouldn't 'integers >6' include 2, and 3-digit (and more) integers? Like 10, 11, 12..50..? How did you decide to use only single digits?