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# Fastest way to solve this units digit question

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Intern
Joined: 06 Oct 2010
Posts: 40
Followers: 0

Kudos [?]: 5 [0], given: 29

Fastest way to solve this units digit question [#permalink]  17 Oct 2010, 11:50
00:00

Difficulty:

5% (low)

Question Stats:

74% (01:13) correct 26% (00:03) wrong based on 34 sessions
Hi. What do you think is the fastest way to solve this question:

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
Manager
Joined: 03 Sep 2010
Posts: 75
Location: Israel
GMAT 1: 660 Q47 V34
GMAT 2: 670 Q48 V34
GPA: 3.2
WE: Operations (Non-Profit and Government)
Followers: 3

Kudos [?]: 26 [2] , given: 2

Re: Fastest way to solve this units digit question [#permalink]  17 Oct 2010, 13:32
2
KUDOS
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.
Intern
Joined: 06 Oct 2010
Posts: 40
Followers: 0

Kudos [?]: 5 [0], given: 29

Re: Fastest way to solve this units digit question [#permalink]  17 Oct 2010, 16:03
Awesome! I think that explanation will help me solve a lot of "units digit" questions. Thanks!
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2794
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 182

Kudos [?]: 1009 [1] , given: 235

Re: Fastest way to solve this units digit question [#permalink]  17 Oct 2010, 16:25
1
KUDOS
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: Fastest way to solve this units digit question   [#permalink] 17 Oct 2010, 16:25
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