In each of the following replace * by (i) the smallest digit (ii) the greatest digit so that the number formed is divisible by 6:

(a) 2*4706

(b) 5825*34

For a number to be divisible by 6, it must be divisible by both 2 and 3.

(a) 2*4706

Last digit is 6, so the number is divisible by 2.

Sum of given digits (except *) = 2 + 4 + 7 + 0 + 6 = 19.

We need 19 + * to be divisible by 3.

The values of * which make 19 + * divisible by 3 are 2, 5 and 8.

(i) The smallest digit is 2. The number formed is 224706.

(ii) The greatest digit is 8. The number formed is 284706.

(b) 5825*34

Last digit is 4, so the number is divisible by 2.

Sum of given digits (except *) = 5 + 8 + 2 + 5 + 3 + 4 = 27.

We need 27 + * to be divisible by 3.

The values of * which make 27 + * divisible by 3 are 0, 3, 6 and 9.

(i) The smallest digit is 0. The number formed is 5825034.

(ii) The greatest digit is 9. The number formed is 5825934.