If the number A9257B684 is divisible by 11, then what is the least value of A - B?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. -8.
To be divisible by 11, the difference of the sum of digits of a number at an even place and an odd place either be 0 or a multiple of 11.
For the number A9257B684
Sum of digits at even place = (9 + 5 + B + 8) = 22 + B
Sum of digits at odd place = (A + 2 + 7 + 6 + 4) = 19 + A
Now,
Case (1), when both sums are equal
⇒ A + 19 = B + 22
⇒ (A - B) = 3
⇒ Case (2), when the difference of the sums is 11
⇒ A + 19 - (B + 22) = 11
⇒ A + 19 - B- 22 = 11
⇒ A - B - 3 = 11
⇒ (A - B) = 14
The smallest value of (A - B) will be 3
Case (3), when the difference of the sums is 11
⇒ B + 22 - (A + 19) = 11
⇒ B + 22 - A - 19 = 11
⇒ B - A + 3 = 11
⇒ B - A = 8
⇒ (A - B) = -8
So the Smallest value of (A - B) is -8