# Moderate Number System Solved QuestionAptitude Discussion

 Q. How many natural numbers below 660 are divisible by 5 and 11 but not by 3?
 ✔ A. 8 ✖ B. 9 ✖ C. 10 ✖ D. 11

Solution:
Option(A) is correct

If the number is divisible by 5 and 11 it must be divisible by 55.

The numbers are less than 660.

Hence, dividing 659 by 55 gives the number of multiples of 55 = 11 (ignoring fraction part).

The 11 multiples of 55 which are less than 560, but of these 11 multiples some can be multiples of 3.

The numbers of such, multiples is the quotient of 11 by 3.
Quotient of $\dfrac{11}{3} = 3$.
Out of 11 multiples of 55, 3 are multiples of 3.

Hence, numbers less than 660 and divisible by 5 and 11 but not by $3 = 11-3 =8$

## (3) Comment(s)

Erithlon
()

Let's first calculate the total numbers under 650 that are divisible by 11,3,5. This is calculated as $$649/LCM (11,3,5) = 649/165 = 4(apprx) .... (1)$$

Now, if we take the 11 & 5, it should gives us the total numbers that are under 650 and are divisible by 11,5. This is calculated by

$$649/LCM(11,5) = 649/55 = 12(apprx)....(2)$$

Subtracting (1) from (2) give us the total number of integers that are divisible by 11 & 5 but not 3.

Kshitij Joshi
()

HI 55,110,165,220,275,330,385,440,495,550,605,660 are the numbers which are divisible by 5 and 11.. Which are the multiple of 55.. In this if we are considering below 660 then we have exclude 660.

Now in this list 165,330,495 are divisible by 8. So remaining are not. Hence 11-3=8 is the answer

Shubham
()

I am not able to understand the logic of dividing \$11/3 for finding how many numbers are divisible by 3