Question

The total number of four-digit numbers such that each of first three digits is divisible by the last digit is equal to ______.

Options

• 1086

• 1087

• 1088

• 1089

Answer 1

The total number of four-digit numbers such that each of first three digits is divisible by the last digit is equal to 1086.

Explanation:

Let pqrs is four-digit number.

So, first three-digit pqr should be divisible by ‘s’

If s = 1, then number of required 4 digit number = 9 × 10 × 10

If s = 2, then number of required 4 digit number = 4 × 5 × 5

If s = 3, then number of required 4 digit number = 3 × 4 × 4

If s = 4, then number of required 4 digit number = 2 × 3 × 3

If s = 5, then number of required 4 digit number = 1 × 2 × 2

If s = 6, 7, 8, 9, then number of required 4 digit number = 4 × 4

∴ Total 4 digit required number = 900 + 100 + 48 + 18 + 4 + 16 = 1086