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What is the last digit of

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What is the last digit of [#permalink] New post 11 Jan 2010, 13:50
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (00:33) wrong based on 5 sessions
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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Re: What is the last digit of ...? (GMATClub test m10, q36) [#permalink] New post 11 Jan 2010, 16:18
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 ...? (GMATClub test m10, q36)   [#permalink] 11 Jan 2010, 16:18
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