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What is the units digit of 13^4*17^2*29^3?

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What is the units digit of 13^4*17^2*29^3? [#permalink] New post 17 Oct 2010, 11:50
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

70% (01:27) correct 30% (00:32) wrong based on 94 sessions
What is the units digit of 13^4*17^2*29^3?

(A) 9
(B) 7
(C) 5
(D) 3
(E) 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 May 2015, 01:44, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the units digit of 13^4*17^2*29^3? [#permalink] New post 17 Oct 2010, 13:32
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I think that the fastest and more important, the safest way to solve this is:
First brake the problem to three multiplication problems:
1. 13*13*13*13
2. 17*17
3. 29*29*29
In all of the problems we don't have to multiply by the whole number, but only by the last digit (because that is what we are asked about).
Second, simply multiply: 13*13*13*13. It is actually 3*3*3*3 (we are interested in the last digit). Thus - 3*3=9, 9*3=7(the last digit), 7*3=1 (the last digit).
17*17 is actually 7*7 = 9 (the last digit).
29*29*29 is actually -9*9*9- that can be interpreted into 9*9=1 (the last digit) and 1*9=9.
So eventually we will have- 9 (29^3) * 9 (17^2) * 1 (13^4). Therefore - 9*9=1(the last digit), 1*1=1

So the correct answer is E -1.
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Re: What is the units digit of 13^4*17^2*29^3? [#permalink] New post 17 Oct 2010, 16:03
Awesome! I think that explanation will help me solve a lot of "units digit" questions. Thanks!
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Re: What is the units digit of 13^4*17^2*29^3? [#permalink] New post 17 Oct 2010, 16:25
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General rule :

To find the unit's digit- find the remainder when divided by 10.

to find the last two digits - find the remainder when divided by 100.

....and so on.

For advance theory of remainders check the Math book of gmat Club.
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Re: What is the units digit of 13^4*17^2*29^3? [#permalink] New post 03 May 2015, 23:24
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just need unit digit of every component and multipy them

3^1=3
3^2=9
3^3=7
3^4=1, it is first digit

7^2=9, it is second digit

9^3=9, it is third digit

1*9*9=1

E
Re: What is the units digit of 13^4*17^2*29^3?   [#permalink] 03 May 2015, 23:24
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What is the units digit of 13^4*17^2*29^3?

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