Using the information in statement 1, you end up with 3^10 + m/10. You don’t even need to solve the problem, because the remainder will differ depending on what m is. I would say it is insufficient.

Using the information in statement 2, you end up with 3^4n + 2 in the first terms. Let’s just work with that first term. 4n + 2 can be rewritten as 2(2n + 1) giving you 9^2n +1 added the 1 and divided by 10. Even if you pull something like multiplying 3 x 3 x 3 x 3 x 3 x 3 (which isn’t exactly correct to do) you still end up with n as an unknown.

Taking the two statements together you end up with 3^10 + 1/10 which gives a remainder of, I think, a zero.

So, I would say that the answer is C. But, that seems too easy.

I will leave my previous explanation as an example of how I went in the wrong direction.

When you take 3 to a power of 1, 2, 3, 4, and 5 you end up with a repeating units digit in the pattern:

3^1 = 3
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3 again

Therefore, if n is 1 then the units digit is 9, when n is 2 the units digit is 9, when n is 3 the units digit is 9, when n is 4 the units digit is 9.

Therefore, the result will be divisible by 10 as long as you add a 1 to the first term. Therefore, you just need to know what m is. The answer should be B.

Can you explain how (B) is the correct answer?

How is it that when you don't know the value of 'm', you can still determine the remainder?

I think I am missing something..

What is the OA?

Sorry..figured it out

Reduce the given data. You get something like 9.81^n + m

Any power of 81 will have units digit of 1. So the product (9.81^n) will have a units digit of 9.

Given the 1st piece of info, you have no clue as to what the numerator and hence the remainder would be upon division by 10. So insufficient.

But given the 2nd piece of info we can clearly say that the numerator will be a multiple of 10, since units digit is 9 and m is 1. Hence sufficient.

Hence answer is B.