The remainder when 40 + 41 + 42 + 43 + ........ + 440 is divided by 17 is:
A. 0
B. 16
C. 4
D. 8
E. None of these
Answer: Option E
Solution(By Examveda Team)
Let S be the sum of the expression, ThenS = 40 + 41 + 42 + 43 + ........ + 440
S = (1 + 4 + 16 + 64) + 44 (1 = 4 + 16 + 64) + ...... + 436 + 440
Since, (1 + 4 + 16 + 64) = 85, is divisible by 17. Hence, except 440 remaining expression is divisible by 17.
Thus,
$$\frac{{{4^{40}}}}{{17}} \to \frac{{{{\left( {{4^4}} \right)}^{10}}}}{{17}} \to \frac{{{1^{10}}}}{{17}}$$
Hence, remainder = 1
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
Join The Discussion