Question

Consider a set of integers 1 to 500. Find.

1: How many of these nos. are divisible by 3 or 5 or by 11?
2: Also indicate how many are divisible by 3 or by 11 but not by all 3, 5 and 11?
3: How many are divisible by 3 or 11 but not by 5?​

Answer 1

Answer:

1 to 500 integer divisible by 3 or by 5 or by 11

Answer 2

Answer:

Step-by-step explanation:

Given that ,

a set of integers from 1 to 500.

To find the ,

(1) How many of these numbers are divisible by 3 or 5 or 11.

(2) Also indicate how many are divisible by 3 or by 11 but not by all 3 , 5 and 11.

(3) How many are divisible by 3 or 11 but not by 5.

So,

(1) How many of these numbers are divisible by 3 or 5 or 11.

The number divisible by 3  is 166.

     500 / 3 = 166 + 2

The number divisible by 5 is 100.

     500 / 5 = 100

The number divisible by 11 is 45.

     500 / 11 = 45 + 5

The number divisible by 3 or 5 or 11 is ( 166 + 100 + 45 )

                                                              = 311

(2) Also indicate how many are divisible by 3 or by 11 but not by all 3 , 5 and 11.

The number divisible by 3 is 166.

   500 / 3 = 166 + 2

The number divisible by 11 is 100.

   500 / 11 = 45 + 5

The number divisible   by 3, 5, 11 are 3.

  500/ (3*5*11) = 3 + 5

Therefore, the number divisible by 3 or 11 but not by all 3 , 5 , 11 is ( 166+ 45 ) - ( 3)

 => 211 - 3

 => 208

(3) How many are divisible by 3 or 11 but not by 5.

    The number divisible by 3 are 166.

           500/3 = 166 + 2

   The number divisible by 11 are 45.

            500/11 = 45 + 5

  The number divisible by 3 or 11 but not by 5 = ( 166 + 45 )

                                                                            => 211.

THANKS.

#SPJ3.

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