Question

the number of integers between 1 to 250 which are divisible by 7 or 11​

Answer 1

Answer:

1234567890784848484048484848

Answer 2

The number of integers between 1 to 250 which are divisible by 7 or 11 are 54

Given :

The integers between 1 to 250

To find :

The number of integers between 1 to 250 which are divisible by 7 or 11

Solution :

Step 1 of 3 :

Write down the given integers

We have to find the the number of integers between 1 to 250 which are divisible by 7 or 11

Let ,

A : The set of integers between 1 to 250 which are divisible by 7

B : The set of integers between 1 to 250 which are divisible by 7

Then ,

A ∩ B : The set of integers between 1 to 250 which are divisible by 7 and 11

⇒ A ∩ B : The set of integers between 1 to 250 which are divisible by 77

Step 2 of 3 :

Calculate n(A) , n(B) & n(A ∩ B)

$\displaystyle \sf{ n(A) = \bigg[ \frac{250}{7} \bigg] = \bigg[ 35.71 \bigg] = 35}$

$\displaystyle \sf{ n(B) = \bigg[ \frac{250}{11} \bigg] = \bigg[ 22.72 \bigg] = 22}$

$\displaystyle \sf{ n(A \cap B) = \bigg[ \frac{250}{77} \bigg] = \bigg[ 3.24 \bigg] = 3}$

Step 3 of 3 :

Calculate the number of integers between 1 to 250 which are divisible by 7 or 11

The number of integers between 1 to 250 which are divisible by 7 or 11

= n(A ∪ B)

= n(A) + n(B) - n(A ∩ B)

= 35 + 22 - 3

= 54

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