Question

By which of the following numbers is $1^{11}$ + $2^{11}$+ $3^{11}$+ $4^{11}$ essentially divisible:

• A. 5
• B. 7
• C. 11
• D. 3

Answer 1

The correct option is A 5

Ones digit in $1^{11}$ = 1

Ones digit in $2^{11}$ = 8

Ones digit in $3^{11}$ = 7

Ones digit in $4^{11}$ = 4

Sum = 1 + 8 + 7 + 4 = 20
So, ones digit in $1^{11}$ + $2^{11}$+ $3^{11}$+ $4^{11}$ = 0

$\therefore$ The sum is essentially divisible by 5 or 10.
From the given options, the sum is divisible by 5.