Fill in the blank with a digit such that the resulting number is divisible by 11.

(a) 362,375,__35

(b) 82,919,__21

(c) 57,13__,473

Answer: Hence, a) 0, b) 2, and c) 0

Step-by-step explanation:

As we know that If the difference of sum of odd places values and sum of even places value is divisible by 11, then the number is itself divisible by 11.

(a) 362,375,__35

Sum of odd places values : 3+2+7+5+x=17+x

Sum of even places values : 6+3+5+3=17

Difference between them is 17+x-17=x

So, x should be 0 to get divisible by 11 as 0 is divisible by 11.

(b) 82,919,__21

Sum of odd places values : 8+9+9+2=28

Sum of even places values : 2+1+x+1=4+x

Difference between them is 28 - (4-x) = 24-x

So, x should be 2 so, that it becomes 24-2=22 which is divisible by 11.

(c) 57,13__,473

Sum of odd places values : 5+1+x+7=13+x

Sum of even places values : 7+3+4+3=17

Difference between them is 17 - (13+x) = 4-x

So, x should be 4 so that it becomes 4-4=0 which is divisible by 11.

Hence, a) 0, b) 2, and c) 0