Question

 How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

Answer 1

Number between 10 and 300, which when divided by 4 leave a remainder 3 will be 11, 15, 19, 23,...299
Here, a = 11, d = 15 – 11 = 4, l = 299
∴ T_n = l = a + (n – 1)d
299 = 11 + (n –1) x 4
⇒ 299 – 11 = (n – 1)4
4(n – 1) = 288
⇒ n – 1 = `(288)/(4)` = 72
∴ n = 72 + 1
= 73.