Question

How many 5-digit numbers are there that are divisible by either 45 or 60 but are not divisible by 90?

Answer 1

Answer:

2500 numbers

Step-by-step explanation:

Problem;

 Solving for the number of 5-digit numbers divisible either by 45 or 60 but not divisible by 90;

 Let us approach this in a step wise manner;

  5 -digits numbers ranges from 10,000 to 99,999

To solve this problem, let us find the number of digits that are divisible by 45;  

  the first number divisible by 45 within this range is 10035

   the last number divisible by 45 in this range is 99990

    increment is 45

The total number in this range is:

           $\frac{last number - first number}{increment}$  + 1  = $\frac{99990 - 10035}{45}$  + 1

                                                      =  2000 numbers

To solve this problem, let us find the number of digits that are divisible by 60;  

  the first number divisible by 60 within this range is 10020

   the last number divisible by  in this range is 99960

    increment is 60

$\frac{99990 - 10080 }{90}$

The total number in this range is:

               $\frac{last number - first number}{increment}$  + 1  = $\frac{99960 - 10020}{60}$  + 1  

                                                         =  1500 numbers

To solve this problem, let us find the number of digits that are divisible by 90;  

  the first number divisible by 90 within this range is 10080

   the last number divisible by  in this range is 99990

    increment is 90

The total number in this range is:

         $\frac{last number - first number}{increment}$ + 1  = $\frac{99990 - 10080}{90}$ + 1

                                                  = 1000 numbers

Now solution:

  Number of 5 digits  = number of 45  + number of 60 - number of 90

                                       = 2000 + 1500  - 1000

                                        = 2500 numbers