If 3-digit number 24y is a multiple of 3, then find the value of y?

1.	If 3-digit number 24y is a multiple of 3, then find the value of y?
Answer» Given three digit number = 24y ∴Sum of digits = 2 + 4 + y = 6 + y But it is given that 6 + y is a multiple of 3, the possible values of 6 + y are 6, 9, 12, 15, …. etc. If 6 + y = 6, then y = 6 – 6 = 0 If 6 + y = 9, then y = 9 – 6 = 3 If 6 + y = 12, then y – 12 – 6 = 6 If 6 + y = 15, then y = 15 – 6 = 9 If 6 + y = 18, then y = 18 – 6 = 12 But y is a digit so y ≠ 12 Therefore, the values of y are 0, 3, 6, 9

Answer»

Given three digit number = 24y

∴Sum of digits = 2 + 4 + y = 6 + y

But it is given that 6 + y is a multiple of 3, the possible values of 6 + y are 6, 9, 12, 15, …. etc.

If 6 + y = 6, then y = 6 – 6 = 0

If 6 + y = 9, then y = 9 – 6 = 3

If 6 + y = 12, then y – 12 – 6 = 6

If 6 + y = 15, then y = 15 – 6 = 9

If 6 + y = 18, then y = 18 – 6 = 12

But y is a digit so y ≠ 12

Therefore, the values of y are 0, 3, 6, 9

Discussion