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# Remainder

Author Message
Director
Joined: 23 May 2008
Posts: 756

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15 May 2009, 09:37
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:00) correct 0% (00:00) wrong based on 0 sessions

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gmatee wrote:
What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

6^15 ends in 6
7^4 ends in 1
9^3 ends in 9

6-1=5

5-9 or 15 -9 after carrying 10 =6

C

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SVP
Joined: 29 Aug 2007
Posts: 2452

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15 May 2009, 12:12
bigtreezl wrote:
gmatee wrote:
What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

6^15 ends in 6
7^4 ends in 1
9^3 ends in 9

6-1=5

5-9 or 15 -9 after carrying 10 =6

C

Correct. This is how it is supposed to be solved.

gmatee wrote:
Why do u carry 10?
it may ends in 4 or 6.
Consider this:
155 - 99 = 56
15 - 99 = -84

Reminder can never be in -ve. 15 - 99 = -84 is not correct.

In this case, 6^15 is way larger than (7^4 + 9^3). So there is no question of -ve reminder.
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SVP
Joined: 29 Aug 2007
Posts: 2452

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16 May 2009, 13:36
gmatee wrote:
thanks tiger, but the question now is changed to : is 6^15 > 7^4 + 9^3 ?it is tough for me too

Thats much easier: Its true that 6^15 > 7^4 + 9^3 because 6^15 is way larger than (7^4 + 9^3).
It is always true that n^(n+1) > (n+1)^n for all n>2.

Moreover, the issue here is not of addition rather multiplication. In that case, 6^15 is way greater than (7^4 * 9^3).
Therefore, 6^15 is undoubtdly even greater than (7^4 + 9^3).
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

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Manager
Joined: 15 May 2009
Posts: 167

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16 May 2009, 16:22
gmatee wrote:
What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

Units digit of 6^15 is 6;
for 7^4 it'll be 1;
for 9^3 it'll be 9;

XXXX6-XXXX1-XXXX9 = XXXX6; Thus answer is (C).
SVP
Joined: 29 Aug 2007
Posts: 2452

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17 May 2009, 08:28
gmatee wrote:
ok,i think 6^15 - 7^4 - 9^3 > 0 in the first place (guessing).
btw, how do u know n^(n+1) > (n+1)^n for all n>1, what if n=2, then 8>9?

Thanks for the good catch.

That should be n>2. I updated my earlier post.

--== Message from GMAT Club Team ==--

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

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Re: Remainder   [#permalink] 17 May 2009, 08:28
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