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# What is the last digit of

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Intern
Joined: 25 Oct 2009
Posts: 24
Schools: Wharton, HBS, Stanford
What is the last digit of [#permalink]

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11 Jan 2010, 14:50
00:00

Difficulty:

(N/A)

Question Stats:

50% (00:00) correct 50% (00:33) wrong based on 6 sessions

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What is the last digit of $$9^1+99^2+999^3+...+(10^n-1)^n$$?

(1) n is even
(2) n is prime

OA is
[Reveal] Spoiler:
A

OE:
[Reveal] Spoiler:
We have the sum of integers:

$$(..9) + (..1) + (..9) + (..1) + ...$$

Statement (1) by itself is sufficient. If n is even then this sum ends with 0. If it's odd, then this sum ends with 9.

Statement (2) by itself is insufficient. (2 is prime and even, 3 is prime and odd)

Question:
[Reveal] Spoiler:
it seems from question's stem that n>3, which combined with Statement (2) means that n is odd. As a result, the sum always ends with 9. If this correct, the answer should be D.

Please, give you opinion.
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Joined: 05 Aug 2008
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Schools: Ross 2012
WE 1: 5 Years at Fortune 50 Company in Manufacturing
Re: What is the last digit of ...? (GMATClub test m10, q36) [#permalink]

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11 Jan 2010, 17:18
1
KUDOS
You make an interesting point. I think the idea is that N doesn't have to be greater than 3. Although the question has n being at least 3. I think in it's written form, with the ..., N can be one, two, or three. Which is why it is not sufficient.

Also for Data Sufficiency. The two statements cannont be contridictory. So if you were to use like a) and line b) both statements would be contridictory with since the number cannot be prime and even and greater than 3. so your assumption of n>3 is wrong.
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Re: What is the last digit of [#permalink]

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11 Mar 2016, 21:54
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Re: What is the last digit of   [#permalink] 11 Mar 2016, 21:54
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# What is the last digit of

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