What is the sum of the remainders when the first 30 positive

This topic has expert replies
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

What is the sum of the remainders when the first 30 positive integers are divided by 5?

A. 50
B. 55
C. 60
D. 65
E. 70

User avatar
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Wed Jun 20, 2018 9:11 am
Location: Chicago, IL
GMAT Score:770

by arosman » Wed Jun 20, 2018 1:43 pm
Remainder problems often have a pattern to them. Name of the game is then find the pattern.

1/5 = 0R1
2/5 = 0R2
3/5 = 0R3
4/5 = 0R4
5/5 = 1R0
6/5 = 1R1
7/5 = 1R2
Etc.....................

Each cycle has a sum of 0+1+2+3+4 = 10. We have 6 cycles ---------> 10 * 6 = 60

Answer: C
Adam Rosman, MD
University of Chicago Booth School of Business, Class of 2020
[email protected]

Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock.
https://www.alldaytestprep.com

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Wed Jun 20, 2018 4:25 pm
Max@Math Revolution wrote:[GMAT math practice question]

What is the sum of the remainders when the first 30 positive integers are divided by 5?

A. 50
B. 55
C. 60
D. 65
E. 70
1/5 = 0 R 1, 2/5 = 0 R 2, 3/5 = 0 R 3, 4/5 = 0 R 4, 5/5 = 1 R 0

We see that when the first 5 positive integers are divided by 5, the remainders are 1, 2, 3, 4, and 0, respectively. So the sum of these remainders is 10.

When the next 5 positive integers (6 to 10, inclusive) are divided by 5, the remainders will also be 1, 2, 3, 4, and 0, respectively. So the sum of the remainders will be 10 also. This is true for every set of 5 consecutive integers: 5n - 4, 5n - 3, 5n - 2, 5n - 1, 5n where n is a positive integer.

We see that the first 30 positive integers are comprised of 6 sets of 5 integers, and each set produces 10 as the sum of the remainders. Thus, the sum of all the remainders when the first 30 positive integers are divided by 5 is 6 x 10 = 60.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage

User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Thu Jun 21, 2018 12:33 am
=>

1, 6, 11, 16, 21 and 26 have remainder 1 when they are divided by 5.
2, 7, 12, 17, 22 and 27 have remainder 2 when they are divided by 5.
3, 8, 13, 18, 23 and 28 have remainder 3 when they are divided by 5.
4, 9, 14, 19, 24 and 29 have remainder 4 when they are divided by 5.
5, 10, 15, 20, 25 and 30 have remainder 0 when they are divided by 5.

The sum of the remainders is
1*6 + 2*6 + 3*6 + 4*6 + 0*6 = ( 1 + 2 + 3 + 4 + 0 ) * 6 = 60.

Therefore, the answer is C.

Answer: C