Question

Trick to know how many numbers between 1000 and 5000 are exactly divisible by 225?

Answer 1

we can get the answer by using Arithmetic Progression method.
The sequence of numbers exactly divisible by 225 between 1000 and 5000 is:
1125, 1350, 1575, 1800,......,4950
now since the numbers in the sequence increase with a constant, therefore it is an AP
=> common difference (d) of the AP = 225

and first term (a) of the AP = 1125

Let K be the last term of the AP
then K = 4950
=> a + (n-1)d = 4950
=> 1125 + (n-1)225 = 4950
=> 1125 + 225n - 225 = 4950
=> 225n = 4950 - 1125 + 225
=> 225n = 4950 - 900
=> n = 4050/225
=> n = 18
therefore there are 18 numbers between 1000 and 5000 that can exactly be divisible by 225