Question

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?
(a) 71
(b) 72
(c) 73
(d) 74

Answer 1

(c) 73

The required numbers are 11, 15, 19, ..., 299.
This is an AP in which a = 11, d = (15 - 11) = 4 and T_n = 299
Now, T_n = 299
⇒ a + (n - 1)d = 299
⇒ 11 + (n - 1) ⨯ ​4 = 299
⇒ 4n = 292
⇒ n = 73
Hence, 73 numbers, which when divided by 4 leave a remainder 3, lie in between 10 and 300.