GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 6

Question

The number of positive integers less than $1000$ which are divisible by $7$ but not by $11$ is $\_\_\_\_$

Answer 1

The number of numbers which are divisible by $7$ and less than $1000 = \lfloor \frac{1000}{7} \rfloor=142$

The number of  numbers which are divisible by $7$ as well as $11 =\lfloor \frac{1000}{7\times 11} \rfloor=12$

$\therefore$ The number of numbers which are divisible by $7$ but not $11 = 142 -12 =130$