What is the value of p such that 579p46 is divisible by 11?

Correct option is D

Given:

Number = 579p46

Concept Used:

Divisibility rule for 11: A number is divisible by 11 if the difference between the sum of its digits

at odd positions and the sum of its digits at even positions is either 0 or a multiple of 11.

Solution:
Number = 579p46
Odd positions: 5, 9, 4
Even positions: 7, p, 6

Sum of odd-position digits = 5 + 9 + 4 = 18
Sum of even-position digits = 7 + p + 6 = 13 + p

For divisibility by 11, the difference between these sums must be a multiple of 11:
(18) - (13 + p) = 5 - p

To be divisible by 11,5 - p should be 0 or a multiple of 11.
Thus, 5 - p = 0 or 5 - p = 11.

Solving for p:

5 - p = 0

Then, p = 5

5 - p = 11

Then, p = -6 (which is not possible for a digit)

Thus, the only valid solution is p = 5.