Question

The average of five consecutive even numbers is 30. What is the
sum of the smallest and the largest among these numbers?
a) 62
b) 60
c) 64
d) 68

Answer 1

Sum of the smallest and the largest is 60 if the average of five consecutive even numbers is 30

Given:

The average of five consecutive even numbers is 30

To Find:

The sum of the smallest and the largest among these numbers

Solution:

Assume that   five consecutive even numbers are

a- 4 , a - 2 , a  , a + 2 , a + 4

Sum of all the numbers = a - 4 + a - 2 + a + a + 2 + a + 4 = 5a

Average = 5a/5  = a

Average = 30

=> a = 30

Sum of smallest and largest = a - 4 + a + 4 =  2a

Substitute a = 30

2a = 2(30) = 60

Hence, sum of the smallest and the largest is 60

Correct option is b) 60

Answer 2

The sum of the smallest and the largest among these numbers = 60

Given :

The average of five consecutive even numbers is 30.

To find :

The sum of the smallest and the largest among these numbers is

a) 62

b) 60

c) 64

d) 68

Solution :

Step 1 of 4 :

Calculate the sum of five consecutive even numbers

Here it is given that the average of five consecutive even numbers is 30.

∴ The sum of five consecutive even numbers

= 5 × 30

= 150

Step 2 of 4 :

Form the equation to find the numbers

Let five consecutive even numbers are x , x + 2 , x + 4 , x + 6 , x + 8

By the given condition

$\displaystyle \sf{ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 150 }$

Step 3 of 4 :

Find the numbers

$\displaystyle \sf{ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 150 }$

$\displaystyle \sf{ \implies 5x +20 = 150 }$

$\displaystyle \sf{ \implies 5x = 150 - 20 }$

$\displaystyle \sf{ \implies 5x = 130 }$

$\displaystyle \sf{ \implies x = \frac{130}{5} }$

$\displaystyle \sf{ \implies x = 26 }$

So five consecutive even numbers are 26 , 28 , 30 , 32 , 34

Step 4 of 4 :

Calculate the sum of the smallest and the largest among these numbers

The smallest among these numbers = 26

The largest among these numbers = 34

The sum of the smallest and the largest among these numbers

= 26 + 34

= 60

Hence the correct option is b) 60

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