Which of the following numbers is divisible by 11?
- A908781
- B969331
- C701611
- D611571
Solution & Step-by-step Explanation
A number is divisible by 11 if the difference between the sum of the digits at odd positions and the sum of the digits at even positions is either 0 or a multiple of 11.
Let's check the options:
Option A) 908781
Sum of odd positions (from right): 1+7+0=8
Sum of even positions (from right): 8+8+9=25
Difference: ∣8−25∣=17 (Not divisible by 11)
Option B) 969331
Sum of odd positions: 1+3+6=10
Sum of even positions: 3+9+9=21
Difference: ∣10−21∣=11 (Divisible by 11)
Option C) 701611
Sum of odd positions: 1+6+0=7
Sum of even positions: 1+1+7=9
Difference: ∣7−9∣=2 (Not divisible by 11)
Option D) 611571
Sum of odd positions: 1+5+1=7
Sum of even positions: 7+1+6=14
Difference: ∣7−14∣=7 (Not divisible by 11)
Thus, 969331 is divisible by 11.
Let's check the options:
Option A) 908781
Sum of odd positions (from right): 1+7+0=8
Sum of even positions (from right): 8+8+9=25
Difference: ∣8−25∣=17 (Not divisible by 11)
Option B) 969331
Sum of odd positions: 1+3+6=10
Sum of even positions: 3+9+9=21
Difference: ∣10−21∣=11 (Divisible by 11)
Option C) 701611
Sum of odd positions: 1+6+0=7
Sum of even positions: 1+1+7=9
Difference: ∣7−9∣=2 (Not divisible by 11)
Option D) 611571
Sum of odd positions: 1+5+1=7
Sum of even positions: 7+1+6=14
Difference: ∣7−14∣=7 (Not divisible by 11)
Thus, 969331 is divisible by 11.