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# Find is the last digit of 3^(3^3) ? A) 1 B) 7 C) 6 D) 3 E) 5

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Manager
Joined: 10 Oct 2005
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Find is the last digit of 3^(3^3) ? A) 1 B) 7 C) 6 D) 3 E) 5 [#permalink]  12 Nov 2005, 10:48
Find is the last digit of 3^(3^3) ?

A) 1
B) 7
C) 6
D) 3
E) 5
Manager
Joined: 04 Oct 2005
Posts: 246
Followers: 1

Kudos [?]: 21 [0], given: 0

3^3 is 27
so we need to find the unit digit if 3^27
find the pattern:
3^1 3
3^2 9
3^3 27
3^4 81
3^5 .....3

the pattern repeats. The pattern repeats every 4 digits. so you know that 3^24 (which is 4*8) will have a unit digit of 1. now you can count three up and see that 3^27 will have a digit of 7
Thus B
Director
Joined: 27 Jun 2005
Posts: 515
Location: MS
Followers: 2

Kudos [?]: 29 [0], given: 0

3^3^27

3^3= 27
3^4=81
3^5=243
3^6=729
3^7= 2187
so it repeats the pattren of 13 97 ...at the last digt.
so 3^11 =....7
3^15
3^19
3^23
3^27=.......7

so at each addition of 4 power the last digt come out to be 7

hence B
Current Student
Joined: 23 Oct 2005
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Schools: Cranfield SOM
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Re: Powers [#permalink]  12 Nov 2005, 13:44
briozeal wrote:
Find is the last digit of 3^(3^3) ?

A) 1
B) 7
C) 6
D) 3
E) 5

Like nero44 I tried finding the pattern by using:

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81

Hence answer for 3^27 = B.
VP
Joined: 06 Jun 2004
Posts: 1059
Location: CA
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Re: Powers [#permalink]  13 Nov 2005, 15:37
briozeal wrote:
Find is the last digit of 3^(3^3) ?

A) 1
B) 7
C) 6
D) 3
E) 5

B for me as well.

Pattern of the last digit is 3, 9, 7, 1, and is repeated every 4 times

3^27 (27/4 = 6R3)

So the last digit is 7.
Senior Manager
Joined: 11 May 2004
Posts: 458
Location: New York
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Kudos [?]: 15 [0], given: 0

Yea, another B.

3^3 = 27

So, 3^27, the pattern goes...3,9,7,1,3,9...

So, the pattern resets after the 4th...
Manager
Joined: 10 Oct 2005
Posts: 52
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Yes OA is B. Thanks Guys !!
VP
Joined: 22 Aug 2005
Posts: 1123
Location: CA
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Everytime I do this problem, I get it wrong
Reason: 3^3 = 9
_________________

Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)

Senior Manager
Joined: 14 Apr 2005
Posts: 419
Location: India, Chennai
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Re: Powers [#permalink]  15 Nov 2005, 01:34
briozeal wrote:
Find is the last digit of 3^(3^3) ?

A) 1
B) 7
C) 6
D) 3
E) 5

We have to evaluate 3^27.
The unit digit of 3^1 = 3
Unit digit of 3^2 = 9
Unit digit of 3^3 = 7 (27)
Unit digit of 3^4 = 1 (81)
Unit digit of 3^5 = 3 (243)
We observe that the unit digits are cyclic, they form the following sequence {3,9,7,1,3,9,1,7,...}
27= 3 mod 4. The third value in the series is 7. Hence B.
Re: Powers   [#permalink] 15 Nov 2005, 01:34
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