Question

The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is

• A. 271

Answer 1

The correct option is A 271
Let $A\to ÷$ by 3
$B\to ÷$ by 5
$C\to ÷$ by 7
$n(A\cup B\cup C)=n\left(A\right)+n\left(B\right)+n\left(C\right)-n(A\cap B)-n(A\cap C)-n(B\cap C)+n(A\cap B\cap C)$
$=\lfloor \frac{500}{3}\rfloor +\lfloor \frac{500}{5}\rfloor +\lfloor \frac{500}{7}\rfloor -\lfloor \frac{500}{15}\rfloor -\lfloor \frac{500}{21}\rfloor -\lfloor \frac{500}{35}\rfloor +\lfloor \frac{500}{105}\rfloor$
$=166+100+71-33-23-14+4=271$