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# Last digit

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Last digit [#permalink]  26 Dec 2009, 18:21
00:00

Question Stats:

0% (00:00) correct 100% (00:14) wrong based on 2 sessions
What is the last digit of \frac{6^8}{2} ?

Try to solve under 10 sec
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PROMO: Are you an exiting GMAT ToolKit (iOS) user? Get GMAT ToolKit 2 (iOS) for only $0.99 (read more) Math: GMAT Math Book ||| General: GMATTimer ||| Chicago Booth: Slide Presentation The People Who Are Crazy Enough to Think They Can Change the World, Are the Ones Who Do. GMAT Club team member Joined: 02 Sep 2009 Posts: 11610 Followers: 1800 Kudos [?]: 9593 [0], given: 828 Re: Last digit [#permalink] 26 Dec 2009, 19:43 walker wrote: What is the last digit of \frac{6^8}{2} ? Try to solve under 10 sec 6 in any integer power >0 has the last digit 6. Integer ending with 6 divided by 2 can have 3 or 8 as last digit. But as 6^8 will be divisible by 4 for sure, divided by 2 it must give the even number, hence 8 is the correct answer. Another solution: \frac{6^8}{2}=\frac{2^8*3^8}{2}=2^7*3^8 Cyclisity of both 2 and 3 is 4, hence 2^7 has the same last digit as 2^3=8 and 3^8 has the same last digit as 3^4=81, hence 8*1=8. I used first approach, took me 11 secs , so maybe there is a shortcut? _________________ CEO Joined: 17 Nov 2007 Posts: 3596 Concentration: Entrepreneurship, Other Schools: Chicago (Booth) - Class of 2011 GMAT 1: 750 Q50 V40 Followers: 231 Kudos [?]: 1300 [3] , given: 346 Re: Last digit [#permalink] 26 Dec 2009, 20:04 3 This post received KUDOS the last digit of 6^n is always 6 (6*6=36). But we cannot simply divide the last digit by 2. So, we can rewrite as: 6^7 * \frac{6}{2} = 6*3 = 18 --> 8 _________________ iOS/Android: GMAT ToolKit - The bestselling GMAT prep app | GMAT Club (free) | PrepGame | GRE ToolKit | LSAT ToolKit PROMO: Are you an exiting GMAT ToolKit (iOS) user? Get GMAT ToolKit 2 (iOS) for only$0.99 (read more)
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Re: Last digit [#permalink]  26 Dec 2009, 20:11
walker wrote:
the last digit of 6^n is always 6 (6*6=36).

But we cannot simply divide the last digit by 2. So, we can rewrite as:

6^7 * \frac{6}{2} = 6*3 = 18 --> 8

There was a shortcut. +1.
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Re: Last digit [#permalink]  26 Dec 2009, 22:35
2 lions in the same jungle.

Thats interesting ....
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Re: Last digit [#permalink]  26 Dec 2009, 22:41
GMAT TIGER wrote:
2 lions in the same jungle.

Thats interesting ....

but you are the only tiger
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Re: Last digit [#permalink]  26 Dec 2009, 23:03
(6^8)/2 = (6/2) * 6*6*6*6*6*6*6
= 3 * 6*6*6*6*6*6*6
= 18 * 6 *6*6*6*6*6

if 18 is multiplied by any no. of 6 last digit will be 8

hence ans 8

I think this is shortest method
Re: Last digit   [#permalink] 26 Dec 2009, 23:03
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