6. How many even prime numbers are there in the set of natural numbers?​

6. How many even prime numbers are there in the set of natural numbers?​

1 thought on “6. How many even prime numbers are there in the set of natural numbers?​”

$$\large{ \boxed{ \rm{ \pmb{ \pink{x = 11}}}}}$$

$$\boxed{ \bf{ \underline{7 : \pink{11} : : 35 : 55 }}}$$

Step-by-step explanation :

• In this question, we are provided with the proportion $$\bf 7 : x : : 35 : 55$$ and we have to find the value of x.

• So, for calculating the value of x, we will apply this method,

$$\boxed{ \tt{ \underline{Product \: of \: means = Product \: of \: extremes }}}$$

• And lastly we will calculate the value of x.

Given :

$$\tt 7 : x : : 35 : 55$$

To Find :

The value of x.

Options given :

5

6

13

11 $$\checkmark$$

Calculations :

We know that,

$$\boxed{ \tt{ \underline{Product \: of \: extremes = Product \: of \: means }}}$$

Putting the values,

$$\mapsto \sf \dfrac{7}{x} = \dfrac{35}{55}$$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$$\mapsto \sf x = \dfrac{55 \times 7}{35}$$

On multiplying the numbers [55 × 7]

$$\mapsto \sf x = \dfrac{385}{35}$$

Performing division,

$$\mapsto \sf x = \cancel \dfrac{385}{35}$$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$$\mapsto \boxed{ \rm{ \pmb{ \red{ x = 11}}}} \$$

Therefore,

The value of x is 11.