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# If n is a positive integer, what is the value of the hundreds digit of

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Math Expert
Joined: 02 Sep 2009
Posts: 51072
If n is a positive integer, what is the value of the hundreds digit of  [#permalink]

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19 Nov 2017, 22:40
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Difficulty:

35% (medium)

Question Stats:

69% (01:23) correct 31% (01:23) wrong based on 182 sessions

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If n is a positive integer, what is the value of the hundreds digit of 30^n ?

(1) 30^n > 1000
(2) n is a multiple of 3

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Joined: 05 Dec 2016
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Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: If n is a positive integer, what is the value of the hundreds digit of  [#permalink]

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19 Nov 2017, 23:21
(1) we can deduce that n>2
30^3=27000
Hundreds digit is Zero
(2) Lowest multiple is 3, so again we can find that hundreds digit is Zero
Intern
Joined: 25 Nov 2017
Posts: 3
Re: If n is a positive integer, what is the value of the hundreds digit of  [#permalink]

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27 Nov 2017, 17:16
Isn't 0 a multiple of 3 though?
Math Expert
Joined: 02 Aug 2009
Posts: 7098
Re: If n is a positive integer, what is the value of the hundreds digit of  [#permalink]

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27 Nov 2017, 17:18
1
kimiah39 wrote:
Isn't 0 a multiple of 3 though?

Yes, 0 is a multiple of 3, but 0 is not a positive integer and it is given that n is a positive integer..
so n cannot be 0
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 25 Nov 2017
Posts: 3
Re: If n is a positive integer, what is the value of the hundreds digit of  [#permalink]

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27 Nov 2017, 17:21
chetan2u wrote:
kimiah39 wrote:
Isn't 0 a multiple of 3 though?

Yes, 0 is a multiple of 3, but 0 is not a positive integer and it is given that n is a positive integer..
so n cannot be 0

oh okay great thank you!
Math Expert
Joined: 02 Sep 2009
Posts: 51072
Re: If n is a positive integer, what is the value of the hundreds digit of  [#permalink]

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27 Nov 2017, 20:11
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1
kimiah39 wrote:
Isn't 0 a multiple of 3 though?

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

For more check below:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: If n is a positive integer, what is the value of the hundreds digit of &nbs [#permalink] 27 Nov 2017, 20:11
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