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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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