Question

How many numbers between 1 and 100 (inclusive) are divisible by 3 or 2?

Answer 1

Answer:

100 divided by 3 is 33.333333. This means that there are 33 numbers between 1 and 100 that are divisible by 3. 100 divided by 2 is 50. This means that there are 50 numbers between 1 and 100 that are divisible by 2.

Answer 2

There are 67 numbers between 1 and 100 (inclusive) are divisible by 3 or 2

Given :

The integers between 1 and 100 (inclusive)

To find :

The number of numbers between 1 and 100 (inclusive) are divisible by 3 or 2

Solution :

Step 1 of 3 :

Write down the given numbers

We have to find the the number of numbers between 1 and 100 (inclusive) are divisible by 3 or 2

Let ,

A : The set of numbers between 1 and 100 (inclusive) are divisible by 3

B : The set of integers between 1 and 100 (inclusive) are divisible by 2

Then ,

A ∩ B : The set of integers between 1 and 100 (inclusive) are divisible by 3 and 2

⇒ A ∩ B : The set of integers between 1 and 100 (inclusive) are divisible by 6

Step 2 of 3 :

Calculate n(A) , n(B) & n(A ∩ B)

$\displaystyle \sf{ n(A) = \bigg[ \frac{100}{3} \bigg] = \bigg[ 33.33 \bigg] = 33}$

$\displaystyle \sf{ n(B) = \bigg[ \frac{100}{2} \bigg] = \bigg[ 50 \bigg] = 50}$

$\displaystyle \sf{ n(A \cap B) = \bigg[ \frac{100}{6} \bigg] = \bigg[ 16.66 \bigg] = 16}$

Step 3 of 3 :

Calculate the number of numbers between 1 and 100 (inclusive) are divisible by 3 or 2

The number of numbers between 1 and 100 (inclusive) are divisible by 3 or 2

= n(A ∪ B)

= n(A) + n(B) - n(A ∩ B)

= 33 + 50 - 16

= 67

Hence there are 67 numbers between 1 and 100 (inclusive) are divisible by 3 or 2

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