Number Systems

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sukhman: Master | Next Rank: 500 Posts; Posts: 202; Joined: Sun Sep 08, 2013 11:51 amFollowed by: 2 members; Thanked: 3 times

by sukhman » Thu Oct 17, 2013 12:48 am

1^1+2^2+3^3+...+10^10 is divided by 5. What is the remainder?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

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Source: Beat The GMAT — Problem Solving | Thu Oct 17, 2013 12:48 am

Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Oct 17, 2013 12:52 am

sukhman wrote:1^1+2^2+3^3+...+10^10 is divided by 5. What is the remainder?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Hi Sukhman,

You have already posted the same question earlier,

https://www.beatthegmat.com/number-systems-t270591.html

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mevicks: Master | Next Rank: 500 Posts; Posts: 269; Joined: Thu Sep 19, 2013 12:46 amFollowed by: 7 members; Thanked: 94 times

by mevicks » Thu Oct 17, 2013 12:56 am

sukhman wrote:1^1+2^2+3^3+...+10^10 is divided by 5. What is the remainder?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Is the answer B?

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Oct 17, 2013 12:59 am

mevicks wrote:
sukhman wrote:1^1+2^2+3^3+...+10^10 is divided by 5. What is the remainder?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Is the answer B?

Hi Vivek,
How you concluded OA is B. It should be C.

Regards,
Uva.

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mevicks: Master | Next Rank: 500 Posts; Posts: 269; Joined: Thu Sep 19, 2013 12:46 amFollowed by: 7 members; Thanked: 94 times

by mevicks » Thu Oct 17, 2013 12:59 am

Ah! Got it, the answer is C. Did a silly mistake squaring the unit digits of 8 --> 8 times

Thanks Uva

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Oct 17, 2013 1:01 am

Here is how I did,

Anything to the power of 1 end in =================1
2^2 =================4
3^3 =================7(3,9,7,1)
4^4 =================6(series go like this, 4,6, same again)
5^5 =================5
6^6 =================6
7^7 =================3(7,9,3,1)
8^8 =================6(8,4,2,6)
9^9 =================9(9,1)
10^10 =================0
Sum ends in 7

7/5 leave reminder 2
Hence C

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Oct 17, 2013 1:03 am

mevicks wrote:Ah! Got it, the answer is C. Did a silly mistake squaring the unit digits of 8 --> 8 times

Thanks Uva

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