WORLD PROBLEM

[kwame.appau]

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?

A.33

B.46

C.49

D. 53

E.86

[tommywallach]

Hey Kwame,

A couple things. First off, let's always be careful with our spelling and grammar when writing things in. It's important! (You called this thread "World problem," which I assume you meant as "word problem). Also, always cite sources, so we know where it came from (best to put the source in the title). Where does this come from?

Finally, it's always best to provide a little bit of explanation for where the question caught you up. Even if you had no idea what to do, say that! It's good for us, and anyone else who looks, and it can also help me give the best possible advice.

Now that all that is out of the way, this is a secret remainder question.

"A group of n students can be divided into equal groups of 4 with 1 student left over" = When n is divided by 4, there is a remainder of 1.

Which makes the second part: When n is divided by 5, there is a remainder of 3.

Let's start with the first part. What numbers give you a remainder of 1 when divided by 4? All the numbers that are one more than multiples of 4!:

1 (don't forget, 1/4 has a remainder of 1)
5
9
13
17
21
25
29
33

Now, what numbers have a remainder of 3 when divided by 5? All the numbers that are 3 more than a multiple of 5:

3 (don't forget, 3/5 has a remainder of 3)
8
13
18
23
28
33

Looking at our two tables, we have overlaps at 13 and 33, which are the two smallest values of n:

13 + 33 = 46

The answer is (B).

Hope that makes sense!

-t

[kwame.appau]

yes it is simple explanation. the source is ( Takegre.com)

[tommywallach]

Hey Kwame,

Thanks for letting us know the source. Good luck with your test!

-t