Mathematics
In each of the following replace '*' by a digit so that the number formed is divisible by 9:
(i) 4710*82
(ii) 70*356722
Answer
For a number to be divisible by 9, the sum of its digits must be divisible by 9.
(i) 4710*82
Sum of given digits (except *) = 4 + 7 + 1 + 0 + 8 + 2 = 22.
We need 22 + * to be divisible by 9.
22 + 5 = 27, which is divisible by 9.
Hence, * should be replaced by 5. The number formed is 4710582.
(ii) 70*356722
Sum of given digits (except *) = 7 + 0 + 3 + 5 + 6 + 7 + 2 + 2 = 32.
We need 32 + * to be divisible by 9.
32 + 4 = 36, which is divisible by 9.
Hence, * should be replaced by 4. The number formed is 704356722.
Related Questions
Examine the following numbers for divisibility by 11:
(i) 10428
(ii) 70169803
(iii) 7136985
Examine the following numbers for divisibility by 6:
(i) 93573
(ii) 217944
(iii) 5034126
(iv) 901352
(v) 639210
(vi) 1790184
In each of the following replace '*' by (i) the smallest digit (ii) the greatest digit so that the number formed is divisible by 3:
(a) 4*672
(b) 4756*2
In each of the following replace * by a digit so that the number formed is divisible by 11:
(i) 8*9484
(ii) 9*53762