A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?

86

53

49

46

33

## Divisibility & Prime Number

##### This topic has expert replies

- DanaJ
- Site Admin
**Posts:**2567**Joined:**01 Jan 2009**Thanked**: 712 times**Followed by:**550 members**GMAT Score:**770

4 + 1 = 5 - NO

8 + 1 = 9 - NO

12 + 1 = 13 - YES - first one

16 + 1 = 17 - NO

20 + 1 = 21 - NO

24 + 1 = 25 - NO

28 + 1 = 29 - NO

32 + 1 = 33 - YES - second one

This makes the sum, IMHO, 46.

- franciskyle
- Senior | Next Rank: 100 Posts
**Posts:**32**Joined:**11 Mar 2009**Location:**Whitler, BC, Canada

A quick look and you know that 4 goes into 33 eight times with a remainder of 1. Therefore E.

n = 4k+1 and n=5q+3

Find the smallest number that satisfies this i.e. 13

Therefore the family of numbers will be

a*LCM(4,5) + 13

20a+13

When a=0 the number is 13 which u obtained above

When a = 1 the number will be 33

So 33+13 = 46

Hope this helps!

Regards,

CR

### GMAT/MBA Expert

- Ian Stewart
- GMAT Instructor
**Posts:**2583**Joined:**02 Jun 2008**Location:**Toronto**Thanked**: 1090 times**Followed by:**355 members**GMAT Score:**780

Ah, note that the correct answer shouldn't give the same remainders that are mentioned in the question. The question asks for thefranciskyle wrote:For this one, I would start with deciding which answers gave a remainder of 3 when divided by 5 (the units digit would have to be either 3 or 8 because to be divisible by the units would have to be 0 or 5... add 3 to get 3 and 8 respectively). That leaves us with B & E.

A quick look and you know that 4 goes into 33 eight times with a remainder of 1. Therefore E.

*sum*of two different numbers with certain remainders. We know each of those two numbers will have a remainder of 3 when divided by 5; when we add those two numbers we should now have a remainder of 1 when we divide by 5 (because 3+3 has a remainder of 1). We also want a number with a remainder of 2 when divided by 4, since the two numbers we're adding give a remainder of 1 when divided by 4.

Still, two answer choices remain, unfortunately, so some other method would be needed to choose between 46 and 86.

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

- franciskyle
- Senior | Next Rank: 100 Posts
**Posts:**32**Joined:**11 Mar 2009**Location:**Whitler, BC, Canada