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

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

chetan2u · Answer

5 repeats it's remainder after every 5 numbers..
So it is 1,2,3,4,0,1,2,3,...
30/5=6, so we have 6 sets of 0,1,2,3,4..
Sum of remainders = 6(1+2+3+4)=6*10=60

C

EgmatQuantExpert · Answer

Solution

To find:

• We need to find sum of the remainders when first 30 positive integers are divided by 5.

Approach and Working:

Since the divisor is 5, the remainder will be less than 5 i.e 0, 1, 2, 3, and 4.

We will get remainder as:
 • 1 if we divide 1, 6, 11, 16, 21, and 26 by 5.
• 2 if we divide 2, 7, 12, 17, 22, and 27 by 5.
• 3 if we divide 3, 8, 13, 18, 23, and 28 by 5.
• 4 if we divide 4, 9, 14, 19, 24, and 29 by 5.
• And 0 if we divide 5, 10, 15, 20, 25, and 30 by 5.

Thus, the sum of remainder = 6* = 60.

Hence, option C is the correct answer.
   Answer: C

MathRevolution · Answer

=>

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

ScottTargetTestPrep · Answer

For the first 30 positive integers, we can divide them into 6 sets of 5 consecutive integers, with the last integer in each set a multiple of 5. For example, the first set is {1, 2, 3, 4, 5}.

Let’s divide each integer in the first set by 5: 1/5 = 0 R1 , 2/5 = 0 R2, 3/5 = 0 R3, 4/5 = 0 R4, and 5/5 = 1 R0. The first set has remainders of 1, 2, 3, 4, and 0, and the sum of these remainders is 1 + 2 + 3 + 4 + 0 = 10.

The second set of numbers is {6, 7, 8, 9, 10}, and the pattern of remainders is identical to that of the first set, so the sum of the remainders for the second set will also be 10. In fact, each of the remaining sets of 5 numbers will have the same pattern of remainders and the same sum.

Since there are 6 sets, and since each set has a remainder sum of 10, the sum of all the remainders is 10 x 6 = 60.

Answer: C

BrushMyQuant · Answer

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

Remainders of the number from 1 to 53 when divided by 5 will
 ✤ Repeat in the pattern (1,2,3,4,0) and will
✤ Repeat  \frac{30}{5}  = 6 times

Remainder of 1 by 5 = 1
Remainder of 2 by 5 = 2
Remainder of 3 by 5 = 3
Remainder of 4 by 5 = 4
Remainder of 5 by 5 = 0

=> Sum of Remainders of numbers from 1 to 30 when divided by 5 = 6 * ( 1 + 2 + 3 + 4 + 0) = 6 * 10 = 60

So,  Answer will be C 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards