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Math Revolution GMAT Instructor V
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If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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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

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Originally posted by MathRevolution on 30 Sep 2016, 07:36.
Last edited by MathRevolution on 13 Oct 2016, 19:04, edited 1 time in total.
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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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MathRevolution wrote:
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

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

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.
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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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abhimahna wrote:
MathRevolution wrote:
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

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

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.

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 ?
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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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msk0657 wrote:
abhimahna wrote:
MathRevolution wrote:
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

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

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.

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 ?

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.
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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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MathRevolution wrote:
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

Units digit will always be zero, given the conditions provided in the stem. D
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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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==> 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.

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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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Hi all,

Sorry about the mistake and the question has been edited.
It is supposed to be n is an integer.
Thank you.
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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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2
1
This question is incorrectly tagged as probability .
Abhishek009, you may want to tag this question to Remainders .
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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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

Edited the tags. Thank you.
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Re: If m is 2-digit positive integer and n is a positive integer, what is  [#permalink]

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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" Re: If m is 2-digit positive integer and n is a positive integer, what is   [#permalink] 02 Jul 2019, 11:29
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