Question

the average of two consecutive prime numbers is 30. find the smallest number.

a. 27
b. 28
c. 29
d. 30​

Answer 1

Answer:

c. 29

Step-by-step explanation:

Concept = Prime Numbers

Given= The sum of two consecutive prime numbers

To Find= The smallest among two numbers

Explanation=

We have been the question as the average of two consecutive prime numbers is 30. find the smallest number.

a. 27

b. 28

c. 29

d. 30​

We need to find the correct option.

Since we cannot suppose two prime numbers as x and x+1 because it is not very often that two consecutive numbers are prime normally only exception is 2 and 3 but the average of two is not 30.

So here we check every option and find the other number. If the number is prime and consecutive in prime with respect to the number given it will  be our answer.

Average = Sum of two numbers / 2

30 = Sum of two/2

Sum of two numbers = 30*2 = 60

Checking the numbers sum:

a) Given number 27

    27 +  x = 60

    x = 60-27 = 33.

   Here the number 27 and 33 both are not prime.

b)  Given = 28

    28 + x = 60

    x= 60-28 = 32

   Here also both numbers 28 and 32 are not prime.

c)  Given = 29

    29 + x = 60

    x = 60-29  = 31.

   Here the numbers 29 and 31 both are prime numbers and consecutive in prime also. So we get out numbers here.

Since we need to find the smallest among 29 and 31 we know that 29 is smallest and hence option c is correct.

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