1.

How many number between 1000 and 5000 are exactly divisible by 225?1). 162). 183). 194). 12

Answer»

First multiple of 225 after 1000 is 1125 = 225 × 5

And last multiple of 225 before 5000 is 4950 = 225 × 22

As numbers are DIVISIBLE by 225, they will form an arithmetic PROGRESSION with first TERM 1125 and last term 4950, with common DIFFERENCE 225.

∴ 1st term of this arithmetic progression is 1125

& last term of this arithmetic progression is 4950.

∴ nth term of A.P. = 1st term + (n – 1)d

Where n is number of terms

& d is common difference

⇒ 4950 = 1125 + (n – 1) × 225

⇒ 3825 = (n – 1) × 225

⇒ n – 1 = 17

∴ n = 18

Thus there are total 18 numbers in between 1000 & 5000 which are divisible by 225.


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