QA – Placement Quizzes | Progressions | Question 14

Expression 13n=11/n can also be written as x/13!
What would be the remainder if x is divided by 11?
(A) 2
(B) 4
(C) 7
(D) 9


Answer: (D)

Explanation: We have,
x/13! = 1/1 + 1/2 + 1/3 … + 1/13
x = 13!/1 + 13!/2 + 13!/3 … + 13!/13
Clearly, all the terms in the summation are divisible by 11 except 13!/11.
We can rewrite it as
13*12*11*…*2*1 / 11 = 13*12*10!
We have to find the remainder for 13*12*10! / 11.
But, we know, remainder for ((n-1)!/n) = -1. Then,
Remainder for 13*12*10! / 11 = 2*1*(-1) = -2.
Converting the negative remainder to positive, -2+11 = 9.

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