a 32000-digit number) side by side

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu May 06, 2010 5:15 am

A four digit number 5775 is written 8000 times (i.e. a 32000-digit number) side by side. What is the remainder when this number is divided by 18?
(A) 1
(B) 3
(C) 5
(D) 9
(E) 12

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Source: Beat The GMAT — Problem Solving | Thu May 06, 2010 5:15 am

ps63739: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Apr 20, 2010 9:09 am

by ps63739 » Thu May 06, 2010 5:42 am

You can write the same as (1925 1925 1925 1925 ... 8000)/6 times.

for only 1925 (1st Odd place) you get remainder = 5
For 1925 1925 (even place) you get remainder = 1
For 1925 1925 1925 (3rd place odd) remiainder = 5
Here repeats. So for odd numbers of 1925 you get 5 and for even you get 1
For 8000 times you will get 1.
So answer should be A.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu May 06, 2010 5:47 am

sanju09 wrote:A four digit number 5775 is written 8000 times (i.e. a 32000-digit number) side by side. What is the remainder when this number is divided by 18?
(A) 1
(B) 3
(C) 5
(D) 9
(E) 12

A four digit number 5775 is written 7998 times followed by 8 zero's is divisible by 18 (24*7998 is a multiple of 9)

now we have to worry about the 8 digit number 57755775

Again 57755700 is divisible by 18 (36 is a multiple of 9 and 57755700 is an even number)

now 75/18 leaves a remainder of 3
[spoiler]
B[/spoiler]

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Thu May 06, 2010 5:49 am

5775divided by 18 ..reminder 15
57755775 by 18 ..reminder 3
577557755775 by 18 ..reminder 9
5775577557755775 by 18 ..reminder 15

hence it forms a series of reminder after each 3 times repeat of 5775

hence after 8000 repeat reminder will be 8000%3 or 2 nd term of the series 15,3,9 or 3

Ans option B

can you please provide the ans and explanation..this took me more than 2 minutes

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