If m is 2-digit positive integer and n is a positive integer, what is

Question

If m is 2-digit positive integer and n is an integer, what is the units digit of (2^n)(m)(5^n)?
1) m=17
2) n=3

abhimahna · Answer

(2^n)(m)(5^n) = (10^n)(m)

Now any number multiplied by 10 will always have 0 at the units place.

in the expression above, what ever the value of m is, we will always get 0 at the unit place provided n <> 0.

So, we need to know the value of n only. Only Statement B is sufficient. Hence B.

msk0657 · Answer

I doubt this question.

Since we are clearly given that n is a positive integer...i.e. n can't be a 0. Since  0 is neither positive nor negative integer  (the only one of this kind).

Then obviously the value of n can be from 1 to infinite as per given positive integer condition..whatever the value of n is we always get 0 as the units digit irrespective of m value and n value for this case.

I feel that n is a positive information shouldn't be given...then B is sufficient.

Any thoughts ?

abhimahna · Answer

Yes, correct. n should be given as non negative integer. Then only it would be B.

So, the current question is not GMAT like question.

MathRevolution , please recheck the question and post the corrected one.

Tobybun · Answer

Units digit will always be zero, given the conditions provided in the stem. D

MathRevolution · Answer

==> In the original condition, you get 2 variables(m,n) and the answer is C. However, since this is an integer problem, a key question, if you apply CMT 4(A), when you solve 2), the first digit of (2^3)(m)(5^3) is always 0, so suffi. The answer is B.

Answer B

Answer B

MathRevolution · Answer

Hi all,

Sorry about the mistake and the question has been edited.
It is supposed to be n is an integer.
Thank you.

sb0541 · Answer

This question is incorrectly tagged as probability . 
 Abhishek009 , you may want to tag this question to Remainders .

Bunuel · Answer

Edited the tags. Thank you.

kapstone1996 · Answer

I think I get it, but I need some clarification:

"If m is 2-digit  positive integer  and n is an  integer , what is the units digit of (2^n)(m)(5^n)?"

I get (2^n)(m)(5^n) = (10^n)(M)

So I get anything M * 10^n will result with a 0 in the units digit, but is "1) m = 17" insufficient because N can = a negative number, which will result in 1/10^n, so then the units digit will be 1 (17/10 = 1.7), if n = -1 or even 0 (17/100 = 0.17) if n = -2? So then two different solutions = insufficient.

1) m = 17
2) N = 3, will always be "0"

If m is 2-digit positive integer and n is a positive integer, what is

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