Question

average of 4 consecutive odd numbers is 60 .what is the product of largest and smallest number among these four numbers​

Answer 1

Answer :3591

Given :-

Average of 4 consecutive odd numbers is 60.

To find :-

What is the product of largest and smallest number among these four numbers?

Solution :-

We know that

The general form of an odd number = 2n+1

So the four Consecutive odd numbers are (2n+1),(2n+3),(2n+5),(2n+7)

Sum of these numbers

= (2n+1)+(2n+3)+(2n+5)+(2n+7)

=(2n+2n+2n+2n)+(1+3+5+7)

= 8n+16

We know that

Average = Sum of all observations/Number of all observations

=> Average of these numbers

=> (8n+16)/4

=> 4(2n+4)/4

=> 2n+4

According to the given problem

Average of the consecutive 4 odd numbers = 60

=> 2n+4 = 60

=> 2n = 60-4

=> 2n = 56

=> n = 56/2

=> n = 28

Now,

2n+1 = 2(28)+1 = 56+1=57

2n+3 = 2(28)+3 = 56+3=59

2n+5 = 2(28)+5=56+5 = 61

2n+7 = 2(28)+7 = 56+7 = 63

The four Consecutive odd numbers are 57, 59, 61, 63

The smallest number = 57

The largest number = 63

Their product = 57×63 = 3591

Answer:-

The product of the largest and smallest among these numbers = 3591

Check:-

The four Consecutive odd numbers are 57, 59, 61, 63

Average = (57+59+61+63)/4

=> Average = 240/4

Average = 60

Verified the given relations in the given problem.

Used formulae:-

Average = Sum of all observations /Number of all observations