If the number 76p91 is divisible by 11, calculate the value of p.

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Solution

The correct option is D
7

A number is divisible by 11, if the difference of the sum of its digits in odd places from the right and sum of its digits in even places from the right is 0 or divisible by 11.

Sum of the digits in odd places = 1 + p + 7 = 8 + p

Sum of the digits in even places = 9 + 6 = 15

Difference 8 + p - 15 = p - 7 must be 0 or a multiple of 11

p - 7 = 0, 11, 22, ...

Plug these values

p = 7, 18, 29,...

Since p is a single digit number , hence p = 7

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