NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Multiple Choice Questions
Question 36

Question.  36

Which of the following is divisible by 11?

(A)

1011011

(B)

1111111

(C)

22222222

(D)

3333333

Detailed Answer with Explanation:

Divisibility rule for 11 (simple):

Find the difference between:

• sum of digits in odd places

• sum of digits in even places

If this difference is \(0\) or a multiple of \(11\), the number is divisible by \(11\).

Check each option.

A) 1011011

Odd places digits: \(1,1,0,1\)

Odd sum: \(1+1+0+1 = 3\)

Even places digits: \(0,1,1\)

Even sum: \(0+1+1 = 2\)

Difference: \(3 - 2 = 1\) → not \(0\) or a multiple of \(11\). Not divisible.

B) 1111111

Odd places digits: \(1,1,1,1\)

Odd sum: \(1+1+1+1 = 4\)

Even places digits: \(1,1,1\)

Even sum: \(1+1+1 = 3\)

Difference: \(4 - 3 = 1\) → not \(0\) or a multiple of \(11\). Not divisible.

C) 22222222

Odd places digits: \(2,2,2,2\)

Odd sum: \(2+2+2+2 = 8\)

Even places digits: \(2,2,2,2\)

Even sum: \(2+2+2+2 = 8\)

Difference: \(8 - 8 = 0\) → this is \(0\). So it is divisible by \(11\).

D) 3333333

Odd places digits: \(3,3,3,3\)

Odd sum: \(3+3+3+3 = 12\)

Even places digits: \(3,3,3\)

Even sum: \(3+3+3 = 9\)

Difference: \(12 - 9 = 3\) → not \(0\) or a multiple of \(11\). Not divisible.

Answer: Option C (22222222).

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 1: Number System – Multiple Choice Questions | Detailed Answers