Question

If 10^3n + 2^4k + 1. 9 + k, is divisible by 11, then what is the least positive value of k?

(a) 7

(b) 6

(c) 8

(d) 10

I have been asked this question at a job interview.

I would like to ask this question from The Principle of Mathematical Induction topic in portion Principle of Mathematical Induction of Mathematics – Class 11

Answer 1

Correct answer is (d) 10

To elaborate: P(n) = 10^3n + 2^4k + 1. 9 + k

P(1) = 10^3 + 2^5 . 9 + k

P(1) = 1000 + 288 + k

P(1) = 1288 + k

When 1288 is divided by 11, the remainder is 1.

Therefore, 1287 is divisible by 11.

The next number that is divisible is 1298.

k = 1298 – 1288

k = 10