Question:

When 10 is divided by the positive integer n , the remainder is n-4. Which of the following could be the value of n?

a)3
b)4
c)7
d)8
e)12

The answer is C.

I set up the equation that 10 - ny = n-4
Where y is just some integer for the quotient.

I rearrange this --> 14 = n(y+1)

From here I am stuck.

Can someone please explain what to do next?

Thanks!!

Carla

Quickest way to solve, throw the numbers into the question.

10/3 = 3 remainder 1 ---> No
10/4 = 2 remainder 2 ---> No
10/7 = 1 remainder 3 ---> Yes

Hope that helps!

I have no idea why I got started on building those remainder equations.. your method is just so much more obvious and easy to see..
I really appreciate your help!

Carla

Glad I could be of some help, Carla!

Just a note of caution though - although it is great to test numbers and use trial and error, I think this approach is best used as a default method. Sometimes, trial and error can take much too long.....besides, nothing beats knowing the material and using actual mathematical rules. With that said, if the question looks like testing would work, then go with that!

Good luck on the exam!

Quick citation note: This is from the Official Guide for GMAT Quantitative Review. For copyright reasons, we must cite full source name.