Numbers Divisible by 15

Question

in a set of odd numbers less than 500, What is the total number of numbers divisible by 15?

Comments

Total numbers divisible by 15 below 500 = $\left \lfloor \frac{500}{15} \right \rfloor$ = 33.

Total odd numbers = $\left \lceil \frac{33}{2} \right \rceil$ = 17

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@Kantikumar

What is the logic behind 33/2 ?? is 2 becaause set of odd numbers differs by 2 ?

Had the question been " In a set of numbers which are multiple of 7 "  Then would the answer be 33/ 7 ?

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See, numbers divisible by 15 are in order of 15, 30, 45, 60, so on. We are getting 1 odd then 1 even again odd and even, so on. Therefore we'll have to divide by 2 here.

For multiple of 7 : $\left \lfloor \frac{500}{7} \right \rfloor$ = 71

Odd numbers = $\left \lceil \frac{71}{2} \right \rceil$ = 36

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@Kantikumar

Actually I was asking the other way ,

" In a set of numbers which are multiple of 7 and less than 500 , What is the total number of numbers divisible by 15 "

Here we will divide 33 / 7  , right ?

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Nopes.

Here required number will be multiple of both 7 and 15.

$\therefore$LCM(7,15) = 105

Total numbers divisible by 105 = $\left \lfloor \frac{500}{105} \right \rfloor$ = 4

Total odd numbers = $\frac{4}{2}$ = 2.