Question

If 20a3 is a 4-digit number and a multiple of 3, then sum of the possible values of a is

Answer 1

Since 20a3 is a 4-digit number and a multiple of 3.
So, the sum of all digits of 20a3 will be a multiple of 3.

2 + 0 + a + 3 = 5 + a
5 + a should be a multiple of 3.

If 5 + a = 3
$\Rightarrow$ a = -2
a is a digit of a number and it cannot be negative.

If 5 + a = 6
$\Rightarrow$ a = 1

If 5 + a = 9
$\Rightarrow$ a = 4

If 5 + a = 12
$\Rightarrow$ a = 7

If we take 5 + a = 15 $\Rightarrow$ a = 10 which is a two digit number, but we already know that a is a single digit.

Therefore, possible values of a are 1, 4 and 7.

Required sum = 1 + 4 + 7 = 12