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

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