Question

The sum of nine odd integers is 99. What is average of the greatest and the least integers?

Answer 1

Answer:

7

Step-by-step explanation:

For any set of consecutive integers, average = median. Let the 7 integers be 1, 2, 3, 4, 5, 6, 7. Since k+2 = average = median = 4, k=2. Product of the greatest and least = 7*1 = 7.

Hope it helps you

Answer 2

Answer:

The average of the greatest and the least integer is 11

Step-by-step explanation:

Given that,

The sum of nine odd integers is 99 and we are required to find the average of greatest and least integer of those 9 numbers.

Let the 9 odd numbers be of the form

$(2n+1),(2n+3),.............(2n+17)$

As the sum of numbers is 99,we can write it as follows

$(2n+1)+(2n+3)+.............+(2n+17)=99\\= > 9(2n)+(1+3+5+7+9+11+13+15+17)=99\\= > 18n+81=99\\= > n=1$

Hence the greatest and least integers out of the given numbers are

$2(1)+17=19\\2(1)+1=3$

Now the average of these two integers is calculated as shown below

$Avg=\frac{19+3}{2} =11$

Therefore,the average of the greatest and the least integer is 11

#SPJ3