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

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

by Max@Math Revolution » Fri Sep 30, 2016 6:37 am
If m is 2-digit positive integer and n is a positive integer, what is the units digit of (2^n)(m)(5^n)?
1) m=17
2) n=3
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by Max@Math Revolution » Sun Oct 02, 2016 2:55 am
==> 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
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by gmathundred » Sun Oct 02, 2016 6:14 pm
So isnt (2^n)m(5^n) same as (10^n)m.

Since n is a positive integer so n>=1, m is always multiplied by 10 and m is also an integer. So units digit is always 0. We dont really need m or n for the answer.

where am I going astray here in this thinking
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by gmathundred » Mon Oct 03, 2016 10:01 am
anyone?
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by Brent@GMATPrepNow » Mon Oct 03, 2016 10:15 am
gmathundred wrote:So isnt (2^n)m(5^n) same as (10^n)m.

Since n is a positive integer so n>=1, m is always multiplied by 10 and m is also an integer. So units digit is always 0. We dont really need m or n for the answer.

where am I going astray here in this thinking
You're absolutely correct, gmathundred

(2^n)(m)(5^n) = (10^n)(m)
Since n is a positive integer, 10^n can equal 10, 100, 1000, 10000, 100000, etc
Since m is also a positive integer, we can be certain that the units digit of (10^n)(m) will be zero.
So, as you suggested, this question can be answered without using the statements.
As such, this would never be an actual GMAT question.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Thu Oct 13, 2016 5:36 pm
Hi all,

There has been a mistake.
It is supposed to be "n is an integer" and "positive" should be omitted.
Thank you.
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