If n and m are positive integers

[hitesh.sakkerwal]

If n and m are positive integers, what is the remainder when 3^(4n+2) is divided by 10?

1. n=2
2. m=1

I approached this problem by rephrasing the statement as: finding the unit digit of expression 3^(4n+2) will give me its remainder.

1. n=2: I thought this is sufficient since I could find the unit digit of 3^(10).
2. m=1. No information about the expression is given. So I thought this is insufficient.

But the GMATprep gives its answer as B. I could not understand why. Could you please explain the reasoning for the same?

Thanks!

[atul.prasad]

Hitesh, I guess your questions is incomplete:

it is : what is the remainder when 3^(4n+2) +m is divided by 10

Lets simplify:
3^(4n+2) = (3^2)(3^4n)
= 9 ((3^4))^n
= 9(81)^n
regardless of the value of n, the last digit of 81^n will be 1
hence the last digit of 3^(4n+2) will always be 9 * 1 = 9

Now the remainder when any number is divided by 10 is the last digit of the number.
Hence, for this question we need to know what is the last digit for the number 3^(4n+2) + m:

from our calculations above the digit is (9 + m)%10.
so , n does not have a bearing on what digit it is.

Clearly B is the right answer.

[hitesh.sakkerwal]

Hi Atul,

Thanks for the explanation!. But the question posted is correct.
http://postimage.org/image/1ifm0x6g4/

[atul.prasad]

That's weird Hitesh :). Probably we should ask pearson to correct this.
Here is the correct image for the same which i found on the web.

http://www.postimage.org/image.php?v=gx4jBkFJ

Otherwise, m seems to have no role in the question!!

[hitesh.sakkerwal]

I agree!. How is this possible? I cannot understand. When I saw this question on test, I was wondering that this could be solved without any further information and should be a problem solving one. But it seems otherwise.
anyway, I hope this is not a mistake!. but still wondering for the correctness of the question.

[jnelson0612]

Hi hitesh,
Yes, clearly the problem you posted has a mistake or typo in that it omitted m. Without m, there is absolutely no way to obtain B as the correct answer. I would go with the problem atul has posted as that is clearly the way the problem should read. His explanation is excellent and as long as you understand it I would not worry further about this problem.

Thank you,