Question

Both ABC and 3D8 are three digit numbers such that ABC - 3D8 = 269.

If 3D8 is divisible by 9, then what number does ABC represent?

Answer 1

647

Explanation:

The divisibility rule for 9 can be used to find the unknown number.

Divisibility rule

A number is divisible by 9 if the sum of its digits is divisible by 9.

The number 3D8 will be divisible by 9 when 3 + D + 8 = <multiple of 9>. Since D is a single digit, we must have ...

11 +D = 18

D = 7 . . . . . . . subtract 11

The number 3D8 is 378.

Difference

Now we know that the difference is ...

ABC -3D8 = ABC -378 = 269

ABC = 269 +378 = 647

ABC represents the number 647.