Find the least value digit which is assigned to ∗ so that the number 1972∗471 is divisible by 9.
- A3
- B5
- C4
- D2
Solution & Step-by-step Explanation
A number is divisible by 9 if the sum of its digits is divisible by 9.
Let the missing digit ∗ be x.
Sum of the digits of the number 1972x471:
Sum=1+9+7+2+x+4+7+1
Sum=31+x
For the number to be divisible by 9, (31+x) must be a multiple of 9.
The nearest multiple of 9 greater than or equal to 31 is 36.
Therefore:
31+x=36
x=36−31=5
Thus, the least value digit assigned to ∗ is 5.
Let the missing digit ∗ be x.
Sum of the digits of the number 1972x471:
Sum=1+9+7+2+x+4+7+1
Sum=31+x
For the number to be divisible by 9, (31+x) must be a multiple of 9.
The nearest multiple of 9 greater than or equal to 31 is 36.
Therefore:
31+x=36
x=36−31=5
Thus, the least value digit assigned to ∗ is 5.