Question

How many numbers lie btw 10 and 300 which are dividible by 4 leaving remainder 3?

Answer 1

This question will be solved by Arithmetic Progression.

10, 15 , 19 , 23...... 299, 300

When we divide 15 by 4 then it leaves remainder 3.

So numbers between 10 and 300

15,19,23.......299

first term (a) = 15

Common difference (d) = 19-15 = 4

Now,

$t_{n} = 299$

a + (n-1)d = 299

15 + (n-1)4 = 299

(n-1)4 = 299-15

(n-1)4 = 284

(n-1) = 284/4

n - 1 = 71

n = 72

Hence, 72 numbers will lies between 10 and 300 which leaves remainder 3 when divided by 4.