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Question

# Question 36 Which of the following numbers is divisible by 11? (A) 1011011 (B) 1111111 (C) 22222222 (D) 3333333

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Solution

## A number is divisible by 11 if the difference of the sum of the digits on even places and odd places is either 0 or divisible by 11. From option (a), we get Sum of the digits at even places=1+1+0=2 Sum of the digits at odd places=1+0+1+1=3 Difference=3-2=1 ∴ It is not divisible by 11. From option (b), we get Sum of the digits at even places=1+1+1=3 Sum of the digits at odd places=1+1+1+1=4 Difference=4-3=1 ∴ It is not divisible by 11. From option (c), we get Sum of the digits at even places=2+2+2+2=8 Sum of the digits at odd places=2+2+2+2=8 Difference=8-8=0 ∴ It is divisible by 11. From option (d), we get Sum of the digits at even places=3+3+3=9 Sum of the digits at odd places=3+3+3+3=12 Difference=12-9=3 ∴ It is not divisible by 11. Hence, 22222222 is divisible by 11. Hence the correct answer is option D.

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