Brent@GMATPrepNow wrote:

sohailmbaprep wrote:q)What is the remainder when 7^25 is divided by 6 ?
how do i solve this problem.

We could use some modular arithmetic (https://en.wikipedia.org/wiki/Modular_arithmetic) to solve this, but I believe this would be out of scope for the GMAT.

An easy way is to start testing some values and see if a pattern emerges.
7^1 divided by 6 leaves remainder 1
7^2 divided by 6 leaves remainder 1
7^3 divided by 6 leaves remainder 1
7^4 divided by 6 leaves remainder 1
7^5 divided by 6 leaves remainder 1
.
.
.
I'm going to go out on a limb and conclude that 7^25 divided by 6 leaves remainder 1

Aside: There's a modular arithmetic rule that basically says: If N divided by D leaves remainder R, then the remainder when N^k is divided by D is equal to the remainder when R^k is divided by D. If we apply this rule to the above question, we'll see that the answer is 1.

sohailmbaprep wrote:Questions like these at times become very tricky if they are put in this way
Q)What is the remainder when 7777..56 times is divided by 19?

Pattern time:
7 divided by 19 leaves remainder 7
77 divided by 19 leaves remainder 1
777 divided by 19 leaves remainder 17
7777 divided by 19 leaves remainder 6
77777 divided by 19 leaves remainder 10
Hmmm, I've already done more work than would be reasonable for an official GMAT question. Perhaps we could apply some higher-level modular arithmetic, but as it stands, the question is out-of-score for the GMAT. Unless, I'm totally missing something basic here (which is quite possible )

Cheers,
Brent