Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 22 May 2015, 10:56

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

Author Message
TAGS:
Senior Manager
Joined: 05 Jun 2005
Posts: 455
Followers: 1

Kudos [?]: 22 [0], given: 0

00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
I have a vague idea about this and took a guess and got it right. But I'd like to see some other explanations

I basically thought of since its exponent is an odd number, its last digit will always be odd and then tried seeing a pattern and picked 7 coz if you multiple it 7 times, gets you last digit 7......

What is the last digit of 3^(987)?

1) 1
2) 3
3) 6
4) 7
5) 9
Manager
Joined: 01 Nov 2006
Posts: 70
Followers: 1

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

You did it right.

3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243 and now the ones digit starts repeating. [edit original answer to make more clear]

so the sequence is {3,9,7,1,3,9,7,1,3,9,7,1, ....} so we merely have to find the 987th one in the series. Apparently, each fourth term is a 1 (so term 8 is 1, term 12 is 1, etc..). That means term 984 is a 1, term 985 is a 3, term 986 is a 9, and term 987 is a 7.
Manager
Joined: 01 Nov 2006
Posts: 70
Followers: 1

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

Of course an even more straightforward way of doing it is to recognize that 3^987 is simply

829236496921142476706699495492534678333952425419534289892901481209785342961686496112003849816259353947669184786817089357646445909706263355584372003200075313488935570269211950074115956571513326518146197550677383466919154911284033685809943263099187977900655123287740529620125316135462447582745383623592042654361925760199521859891889158161732532817099423444872173084985440322849485291685258736792319114827459947632739061572907631860285305265724594082011214874384364252979387

and then the ones digit becomes clear.
Senior Manager
Joined: 05 Oct 2006
Posts: 268
Followers: 1

Kudos [?]: 4 [0], given: 0

Re: PS-Last digit [#permalink]  06 Nov 2006, 08:45
ans = 7

powers of3 go in seq of 1,3,9,7...

quote="uvs_mba"]I have a vague idea about this and took a guess and got it right. But I'd like to see some other explanations

I basically thought of since its exponent is an odd number, its last digit will always be odd and then tried seeing a pattern and picked 7 coz if you multiple it 7 times, gets you last digit 7......

What is the last digit of 3^(987)?

1) 1
2) 3
3) 6
4) 7
5) 9[/quote]
Senior Manager
Joined: 05 Jun 2005
Posts: 455
Followers: 1

Kudos [?]: 22 [0], given: 0

joeydvivre wrote:
Of course an even more straightforward way of doing it is to recognize that 3^987 is simply

829236496921142476706699495492534678333952425419534289892901481209785342961686496112003849816259353947669184786817089357646445909706263355584372003200075313488935570269211950074115956571513326518146197550677383466919154911284033685809943263099187977900655123287740529620125316135462447582745383623592042654361925760199521859891889158161732532817099423444872173084985440322849485291685258736792319114827459947632739061572907631860285305265724594082011214874384364252979387

and then the ones digit becomes clear.

Hahaha this is hilarious. What did you use to get this a calculator. I'll fall asleep doing that lol!

Btw guys thanks for the explanation, looks like was on the right track, just needed that surity and you guys confirmed it.

Thanks a ton
VP
Joined: 25 Jun 2006
Posts: 1175
Followers: 2

Kudos [?]: 74 [0], given: 0

D 7.

it is a repeating sequence of 4. find the remainder of 987/4 and get hte unit digit of 3 to that power.
VP
Joined: 15 Jul 2004
Posts: 1473
Schools: Wharton (R2 - submitted); HBS (R2 - submitted); IIMA (admitted for 1 year PGPX)
Followers: 17

Kudos [?]: 117 [0], given: 13

joeydvivre wrote:
You don't have powers of 3 memorized?

Man - apart from good quant skills you seem to have a perfect wherewithal for some scathing humor!!!
Manager
Joined: 29 Aug 2006
Posts: 157
Followers: 1

Kudos [?]: 4 [0], given: 0

tennis_ball wrote:
D 7.

it is a repeating sequence of 4. find the remainder of 987/4 and get hte unit digit of 3 to that power.

now that is both easy to remember and doable in 2 mins...thanks, tennis_ball!
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5077
Location: Singapore
Followers: 22

Kudos [?]: 186 [0], given: 0

last digit runs in this order: 3 -> 9 -> 7 -> 1

987/3 = 246.75 --> So is the third in the series - '7'
Similar topics Replies Last post
Similar
Topics:
I took GMAT recently and got 640 (44 QA + 34 VA). I guess I 1 05 Aug 2011, 05:51
From having a vague idea of what the GMAT is to scoring 760 14 30 Jun 2009, 05:09
I got it right but that was just a wild guess 4 09 Aug 2008, 17:56
Got it correct. But I guess that is largly due to guess. 2 02 Nov 2007, 04:35
I got it right, but took a little longer than I should have 2 28 Sep 2006, 12:14
Display posts from previous: Sort by