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m09 Q32

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m09 Q32 [#permalink] New post 19 Nov 2010, 09:20
00:00
A
B
C
D
E

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(N/A)

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0% (00:00) correct 0% (00:00) wrong based on 0 sessions
What is the last digit of 3^{3^3} ?

(C) 2008 GMAT Club - m09#32

* 1
* 3
* 6
* 7
* 9

3^{3^3} = 3^{27} = ((3^4)^6) * (3^3) = 27 * (81^6)

81^6 ends with 1, so 27*(81^6) ends with 7.
The correct answer is D.


ps. used excel to verify !
I disagree as 3^{3^3} = (3^3)(3^3)(3^3)= 27x27x27
therefore the answer should be 19683 thus B
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Re: m09 Q32 [#permalink] New post 19 Nov 2010, 09:28
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Expert's post
zisis wrote:
What is the last digit of 3^{3^3} ?

(C) 2008 GMAT Club - m09#32

* 1
* 3
* 6
* 7
* 9

3^{3^3} = 3^{27} = ((3^4)^6) * (3^3) = 27 * (81^6)

81^6 ends with 1, so 27*(81^6) ends with 7.
The correct answer is D.


ps. used excel to verify !
I disagree as 3^{3^3} = (3^3)(3^3)(3^3)= 27x27x27
therefore the answer should be 19683 thus B


RULE: If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
a^m^n=a^{(m^n)} and not (a^m)^n, which on the other hand equals to a^{mn}.

So:
(a^m)^n=a^{mn};

a^m^n=a^{(m^n)} and not (a^m)^n.

So, 3^{3^3}=3^{(3^3)}=3^{27}

Cyclicity of 3 in power is four. The units digit of 3^{27} is the same as for 3^3 (27=4*6+3) --> 7.

Answer: D.

Discussed here: last-digit-of-a-power-70624.html and here: m09-74730.html

Hope it's clear.
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Manager
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Re: m09 Q32 [#permalink] New post 20 Nov 2010, 00:16
gotta - makes perfect sense and kudos
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Re: m09 Q32 [#permalink] New post 20 Nov 2010, 09:52
3^1=3
3^2=9
3^3=27
3^4=81
3^5=243

Means after every 4th power, the unit's digit will be repeated.

thus for 27 powers, it will be 27/4= 6 with reminder-3. where units digit is - 7..

Answer:-D
Re: m09 Q32   [#permalink] 20 Nov 2010, 09:52
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