Question

If the three digit number 71a is divisible by 11, find the value of the digit a.

• A. 6
• B. 5
• C. 7
• D. 8

Answer 1

The correct option is B

5

If a number is divisible by 11, the difference between the sum of digits in the even places and the sum of digits in the odd places is 0 or a multiple of 11.
Sum of digits in odd places = 7 + a
Digit in even place = 1
71a is divisible by 11
Therefore, 7 + a – 1 = 0 or 11k (k is any integer)
7 + a – 1 = 0
a = - 6
The digit cannot be negative.
Hence, 7 + a – 1 = 11k
a = 11k - 6
a = 5 or 16 or 27 or ....
Since a is a digit, a = 5.