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# M13-36

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Math Expert
Joined: 02 Sep 2009
Posts: 49993

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16 Sep 2014, 00:50
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Difficulty:

25% (medium)

Question Stats:

83% (00:43) correct 17% (00:34) wrong based on 92 sessions

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If $$x$$ is a positive integer, what is the hundreds digit of $$x^x$$ ?

(1) $$x$$ is divisible by 10.

(2) $$x$$ is even.

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:50
Official Solution:

Statement (1) by itself is sufficient. The hundreds digit of $$x^x$$ will be 0.

Statement (1) by itself is insufficient. The hundreds digit of $$x^x$$ cannot be determined.

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Joined: 15 Jul 2014
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14 Dec 2014, 17:06
since 0 is also divisible by 10, can we not have x = 0?
Math Expert
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15 Dec 2014, 08:15
kritiu wrote:
since 0 is also divisible by 10, can we not have x = 0?

We are given that x is a positive integer and 0 is neither positive nor negative integer.
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17 Dec 2014, 14:48
Couldn't x = 10 (10 is divisible by 10)? If so, the hundreds digit would be 1 (10^10 = 100). Any insight would be helpful...
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Joined: 25 Apr 2012
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17 Dec 2014, 21:18
1
mclark674162 wrote:
Couldn't x = 10 (10 is divisible by 10)? If so, the hundreds digit would be 1 (10^10 = 100). Any insight would be helpful...

X can be any positive multiple of 10 so yes if x=10 then the expression will be 10^10 and hundred digit will be 0 because 10^10= 10*10*10*10*10...10 times= 10000000000

Consider x=20,even then Hundreds digit will be 0
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Joined: 12 Aug 2014
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Location: United States
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18 Dec 2014, 07:48
WoundedTiger wrote:
mclark674162 wrote:
Couldn't x = 10 (10 is divisible by 10)? If so, the hundreds digit would be 1 (10^10 = 100). Any insight would be helpful...

X can be any positive multiple of 10 so yes if x=10 then the expression will be 10^10 and hundred digit will be 0 because 10^10= 10*10*10*10*10...10 times= 10000000000

Consider x=20,even then Hundreds digit will be 0

------------------------

Thanks for clarifying... silly arithmetic mistake on my part
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01 Aug 2018, 05:57
what if 0^0, how do we get the 100th digit?

Bunuel
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01 Aug 2018, 06:11
gsingh0711 wrote:
what if 0^0, how do we get the 100th digit?

Bunuel

We are given that x is a positive integer, so x cannot be 0. 0 is neither positive nor negative integer.

As for 0^0: 0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.
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Re: M13-36 &nbs [#permalink] 01 Aug 2018, 06:11
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# M13-36

Moderators: chetan2u, Bunuel

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