Question

The least digit \(x\) so that the 7-digit number 34x7826 is divisible by 11 is

• A. 9
• B. 8
• C. 7
• D. 6

Hint:

For divisibility by 11, always calculate: \[ (\text{sum of odd-place digits})-(\text{sum of even-place digits}). \] The result must be \(0,\pm11,\pm22,\ldots\)

Answer 1

The Correct Option is C

Concept: A number is divisible by 11 if the difference between the sum of digits in odd places and even places is a multiple of 11.

Step 1: Finding the required sums.
For 34x7826, Odd place digits: \[ 3+x+8+6=17+x \] Even place digits: \[ 4+7+2=13 \]

Step 2: Applying the divisibility rule.
\[ (17+x)-13=x+4 \] This must be a multiple of 11. \[ x+4=11 \] \[ x=7 \] {7}