Please help! Remainder problem

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dimkras: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Aug 18, 2009 11:42 pm

Please help! Remainder problem

by dimkras » Sat Sep 04, 2010 12:11 am

Would appreciate your help with this one:

What is the sum of all remainders obtained when the first 100 natural numbers are divided by 9?

A. 397

B. 401

C. 403

D. 405

E. 399

Tried to solve many times in many ways but I never get any of these answers.

Quote

Source: Beat The GMAT — Problem Solving | Sat Sep 04, 2010 12:11 am

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

by sanju09 » Sat Sep 04, 2010 12:52 am

dimkras wrote:Would appreciate your help with this one:

What is the sum of all remainders obtained when the first 100 natural numbers are divided by 9?

A. 397

B. 401

C. 403

D. 405

E. 399

Tried to solve many times in many ways but I never get any of these answers.

Remainders would appear in the repeating 11 cycles of 1, 2, 3, 4, 5, 6, 7, 8, and 0 uptil 99, and 1 will be the final remainder when 9 would divide 100.

Total of remainders = 11 Ã— (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0) + 1 = 11 Ã— 36 + 1 = [spoiler]397.

A

Choices are not in order, what's the source?[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Quote

dimkras: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Aug 18, 2009 11:42 pm

by dimkras » Sat Sep 04, 2010 1:29 am

Thanks a lot, but can you give a little bit more detailed explanation of your logic. I don't get why there are 11 cycles.

Source is https://free-quiz.4gmat.com/quizzes/math_quiz_17/

Quote

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

by sanju09 » Sat Sep 04, 2010 1:31 am

dimkras wrote:Thanks a lot, but can you give a little bit more detailed explanation of your logic. I don't get why there are 11 cycles.

Source is https://free-quiz.4gmat.com/quizzes/math_quiz_17/

9 could go 11 times in 100

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com