Question

How many natural numbers upto 1155 are divisible by either 5 or 7 but not by 11?

• A. 105
• B. 330
• C. 333
• D. none of these

Answer 1

The correct option is B 330

Numbers divisible by 5 upto 1155 = 231
Numbers divisible by 7 upto 1155 = 165
Numbers which are divisible by both 5 and 7 (i.e., 35) upto 1155 = 33
$\therefore$ Numbers which are exactly divisible by 5 or 7 = (231 + 165) - 33 = 363
Numbers which are divisible by 5 and 11 both (i.e., 55) = 21
Numbers which are divisible by 7 and 11 both (i.e., 77) = 15
Numbers which are divisible by 5, 7 and 11 simultaneously = 3
$\therefore$ Numbers which are only divisible by either 5 and 11 or 7 and 11
= 21 + 15 - 3 = 33
Hence, the number of numbers which are divisible by 5
or 7 but not by 11 = 363 - 33 = 330