Problem Solving

I have a general problem with questions related to factors, multiples, remainders. I would appreciate if someone would share a simple strategy for solving such questions.

This question appeared in one preparation software and i dont understand the logic:

When 777 is divided by a positive integer n, the remainder is 77. how many possibilities are there for n?
2
3
4
5
6

What difficulty would this question be rated?

Appreciate your help.

I think this is a tough question.

777 = nxk + 77

So, 777-77 = 700 is divisible with n

Since the remainder is 77 , n must be bigger than 77

700 = 2x2x5x5x7

So we have 5 numbers to find some numbers that are bigger than 77

without 7, 2x2x5x5 = 100

5x5x2 = 50 and it is less than 77 so can't use it

with 7

7x2x2= 28 ..nope

7x2x2x5 = 140 - that works

7x5x5 = 175 - that works

7x5x5x2 = 350 - that works

7x5x5x2x2 = 700 - that works

So, 100, 140, 175, 350 and 700

I find 5 , but if I miss another number the answer will be 6.

Any takers ?

i got 5 too

5 is the correct answer. i think i need to revise my multiple/factors principles.

Any advices?

5 is the correct answer. i think i need to revise my multiple/factors principles

Manhattan gmat Number Properties book is a good resource.(the 3rd edition that just got published)

Check this out also:

https://www.onlinemathlearning.com/facto ... iples.html

Regards,
Cramya