Question

The first two digits of a 3 digit number are 3 and 7. What are the possible values of the unit's digit if the number is divisible by 3? (2 marks)

Answer 1

For a number to be divisible by 3, the sum of its digits should be equal to a multiple of 3.
(0.5 mark)

The sum of the given digits is 3 + 7 = 10.

Hence, if 2 is in the units digit, the sum of the digits will be 3 + 7 + 2 = 12, which is a multiple of 3.
$\therefore$372 is divisible by 3.
(0.5 marks)

if 5 is in the units digit, the sum of the digits will be 3 + 7 + 5= 15 which is a multiple of 3.
$\therefore$375 is divisible by 3.
(0.5 marks)

if 8 is in the units digit, the sum of the digits will be 3 + 7 + 8 = 18, which is a multiple of 3.
$\therefore$378 is divisible by 3.
(0.5 marks)

So, the possible numbers are 2, 5, 8.