Which of the following numbers is divisible by 11?
- A88,65,987
- B55,78,961
- C88,65,747
- D45,12,458
Solution & Step-by-step Explanation
According to the divisibility rule for 11, a number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or a multiple of 11.
Let's test Option C: 88,65,747
Sum of digits at odd places (1st, 3rd, 5th, 7th from right):
7+7+6+8=28
Sum of digits at even places (2nd, 4th, 6th from right):
4+5+8=17
Difference:
28−17=11
Since 11 is a multiple of 11, the number 88,65,747 is divisible by 11.
Let's quickly check the other options for confirmation:
Option A: 88,65,987⟹(7+9+6+8)−(8+5+8)=30−21=9 (Not divisible)
Option B: 55,78,961⟹(1+9+7+5)−(6+8+5)=22−19=3 (Not divisible)
Option D: 45,12,458⟹(8+4+1+4)−(5+2+5)=17−12=5 (Not divisible)
Let's test Option C: 88,65,747
Sum of digits at odd places (1st, 3rd, 5th, 7th from right):
7+7+6+8=28
Sum of digits at even places (2nd, 4th, 6th from right):
4+5+8=17
Difference:
28−17=11
Since 11 is a multiple of 11, the number 88,65,747 is divisible by 11.
Let's quickly check the other options for confirmation:
Option A: 88,65,987⟹(7+9+6+8)−(8+5+8)=30−21=9 (Not divisible)
Option B: 55,78,961⟹(1+9+7+5)−(6+8+5)=22−19=3 (Not divisible)
Option D: 45,12,458⟹(8+4+1+4)−(5+2+5)=17−12=5 (Not divisible)