Question

(i) Suppose that the division x $÷$ 5 leaves a remainder 4 and the division x $÷$ 2 leaves a remainder 1. Find the ones digit of x.
(ii) A three-digit number 42x is divisible by 9. Find the value of x.

Answer 1

(i) Since x $÷$ 5 leaves a remainder 4, so ones digit of x can be 4 or 9. Also, since x $÷$ 2 leaves a remainder 1, so ones digit must be 9 only.
(ii) Since 42x is divisible by 9, the sum of its digits, i.e. 4 + 2 + x must be divisible by 9.
i.e. 6 + x is divisible by 9
i.e. 6 + x = 9 or 18, .
Since x is a digit, therefore 6 + x = 9 or, x = 3.