Question

If the numbers which are divisible by 5 and the numbers which have 5 as one of the digits are eliminated from 1 to 60, how many numbers would remain?

Answer 1

Answer:

40

Step-by-step explanation:

The one digit numbers that remain are 1, 2, 3, 4, 6, 7, 8, 9.

For the two digit numbers, think about the digits separately.

The first digit must be one of 1, 2, 3, 4.

The second digit must be one of 1, 2, 3, 4, 6, 7, 8, 9 (can't be 0 or 5 since numbers divisible by 5 are eliminated).

So the number of two digit numbers remaining is

( # choices for first digit ) × ( # choices for second digit) = 4 × 8 = 32.

The number of numbers remaining then is

( # one digit numbers remaining ) + ( # two digit numbers remaining )

= 8 + 32 = 40