Remainder when 3^(4n+2) is divided by 10

g_beatthegmat wrote:Encountered this question in the GMAT Prep questions. Please have a look at the attached screenshot.

I feel the answer should be (D) and not (A) or (B) because irrespective of the answer choices, the answer is already available from the question itself.

What say?

I thought the answer would be A. The question was to find the distinct value of the remainder. Its only from statement 1 that we know abt the value of n and hence the remainder.

Statement 2 is irrelevant as the equation has nothing to do with 'm'.

Hence (A).

We need some more opinions

Ah, that's what I though too and marked (A) as the answer while appearing for the prep test. But here's the catch -

From the question, we have 3^(4n+2) / 10.

Numerator
3^(4n+2) can also be written as
=>3^(4n) * 3^2
=>3^(4n) * 9
=>(3^4)^n * 9 { (3^4)^n is same as 3^(4n) }
=>81^n * 9

Now we've reached to a point where we're actually not dependent on n because anything to the power of 81 would end with unit's digit of 1. So value of n does not matter.

But when we multiply the number with unit's digit of 1 with 9, we would get unit's digit as 9. And when this number is divided by 10, the remained is always 9.

Hi g_beatthegmat,

In fact from the statement we can determine the remainder. Remind that the powers of three are cyclic. Every four numbers you get always the same units digit number.

In this case, since 'n' is an integer we know that....

n=1 - 3^6
n=2 - 3^10
n=3 - 3^14
.....

The units digit of any of the above powers of three is 9. So my pick would be (F). A new GMAT option for (F) none of the propositions are needed. Lol.

How can B be the correct choice? This one needs an expert. Definitely!

g_beatthegmat wrote:Encountered this question in the GMAT Prep questions. Please have a look at the attached screenshot.

I feel the answer should be (D) and not (A) or (B) because irrespective of the answer choices, the answer is already available from the question itself.

What say?

I agree with you. The answer will be (D). Irrespective of the value of n or m, the remainder will always be 9.

So both n & m does not matter. So both statements are individually sufficient as both individually don't matter.

But if the equation was 3^(4n+m), then the answer would have been (B).

TYhe question is incomplete. This has been already posted before and the correct equation is 3^(4n+2) + m for which we have to find the remainder.