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# What is the sum of the remainders when the first 50 positive integers

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the sum of the remainders when the first 50 positive integers  [#permalink]

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09 Nov 2017, 00:03
1
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:23) correct 15% (01:27) wrong based on 75 sessions

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[GMAT math practice question]

What is the sum of the remainders when the first 50 positive integers are divided by 5?

A. 60
B. 70
C. 80
D. 90
E. 100

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1217 Location: India GPA: 3.82 What is the sum of the remainders when the first 50 positive integers [#permalink] ### Show Tags 09 Nov 2017, 01:33 MathRevolution wrote: [GMAT math practice question] What is the sum of the remainders when the first 50 positive integers are divided by 5? A. 60 B. 70 C. 80 D. 90 E. 100 $$50$$ positive integers can be visualized as $$10$$ sets of $$5$$ elements each. each of the elements when divided by $$5$$ will have remainders as {$$1,2,3,4,0$$}. Sum of each elements of this set $$=10$$ and we have $$10$$ such sets. so total sum of remainders $$= 10*10 = 100$$ Option E Senior SC Moderator Joined: 22 May 2016 Posts: 2099 What is the sum of the remainders when the first 50 positive integers [#permalink] ### Show Tags 12 Nov 2017, 07:36 1 MathRevolution wrote: [GMAT math practice question] What is the sum of the remainders when the first 50 positive integers are divided by 5? A. 60 B. 70 C. 80 D. 90 E. 100 Remainders, first 10 integers, including 1-5: $$\frac{1}{5}$$ =0 remainder 1, $$\frac{2}{5}$$ =0 remainder 2 $$\frac{3}{5}$$ =0 remainder 3, $$\frac{4}{5}$$=0 remainder 4 $$\frac{5}{5}$$ = 1 remainder 0,$$\frac{6}{5}$$ = 1 remainder 1 $$\frac{7}{5}$$ =1 remainder 2, $$\frac{8}{5}$$ =1 remainder 3 $$\frac{9}{5}$$ =1 remainder 4, $$\frac{10}{5}$$ = 2 remainder 0 For integers 1-10, sum of remainders = 1+2+3+4+1+2+3+4 = 20. That pattern holds: 1 -10: sum = 20 11-20: sum = 20 21-30: sum = 20 31-40: sum = 20 41-50: sum = 20 Total= 100 Answer E Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2830 Re: What is the sum of the remainders when the first 50 positive integers [#permalink] ### Show Tags 12 Nov 2017, 07:44 MathRevolution wrote: What is the sum of the remainders when the first 50 positive integers are divided by 5? A. 60 B. 70 C. 80 D. 90 E. 100 Let's see if we can find a pattern: The remainders when 1, 2, 3, 4, and 5 are divided by 5 are 1, 2, 3, 4, and 0, respectively. We get the same results from numbers 6 to 10, 11 to 15, etc. Thus, the sum of remainders of each set of five numbers is 1 + 2 + 3 + 4 + 0 = 10. Since there are 10 sets of five numbers from 1 to 50 inclusive, the sum of all the remainders is 10 x 10 = 100. Answer: E _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6517 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the sum of the remainders when the first 50 positive integers [#permalink] ### Show Tags 12 Nov 2017, 18:02 => 1, 2, 3, 4, 5 have remainders 1, 2, 3, 4, 0 and the sum of their remainders is 1 + 2 + 3 + 4 + 0 = 10. 6, 7, 8, 9, 10 have remainders 1, 2, 3, 4, 0 and the sum of their remainders is 1 + 2 + 3 + 4 + 0 = 10. 46, 47, 48, 49, 50 have remainders 1, 2, 3, 4, 0 and the sum of their remainders is 1 + 2 + 3 + 4 + 0 = 10. 10 * 10 = 100 Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: What is the sum of the remainders when the first 50 positive integers  [#permalink]

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12 Nov 2017, 22:27
(0+1+2+3+4) ten times
equal to 100
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Re: What is the sum of the remainders when the first 50 positive integers &nbs [#permalink] 12 Nov 2017, 22:27
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