Question

Samuel is learning the divisibility rule of 11.
The rule says, "A number is divisible by 11 if the difference of the sum of the digits in the odd places and the sum of the digits in even places is 0 or a multiple of 11."

Find which of the following numbers is divisible by 11.

• A. 1932
• B. 1782
• C. 1654
• D. 1349

Answer 1

The correct option is B 1782

Divisibility rule of 11:

"A number is divisible by 11 if the difference of the sum of the digits in the odd places and the sum of the digits in the even places is 0 or a multiple of 11."

$For1654:$
Digits in odd places = 1, 5
Digits in even places = 6, 4

Sum of digits in odd places = 1 + 5 = 6
Sum of digits in even places = 6 + 4 = 10

⇒ Difference = 10 – 6 = 4
4 is not a multiple of 11, so 1654 is not divisible by 11.

$For1349:$
Digits in odd places = 1, 4
Digits in even places = 3, 9

Sum of digits in odd places = 1 + 4 = 5
Sum of digits in even places = 3 + 9 = 12

⇒ Difference = 12 – 5 = 7
7 is not a multiple of 11, so 1349 is not divisible by 11.

$For1782:$
Digits in odd places = 1, 8
Digits in even places = 7, 2

Sum of digits in odd places = 1 + 8 = 9
Sum of digits in even places = 7 + 2 = 9

⇒ Difference = 9 – 9 = 0
Since the difference is 0, 1782 is divisible by 11.

$For1932:$
Digits in odd places = 1, 3
Digits in even places = 9, 2

Sum of digits in odd places = 1 + 3 = 4
Sum of digits in even places = 9 + 2 = 11

⇒ Difference = 11 – 4 = 7
7 is not a multiple of 11, so 1932 is not divisible by 11.

Thus, only 1782 is divisible by 11.