In a set of four integers, the average of the two smallest integers is $102$ , the average of the three smallest integers is $103$ , the average of all four is $104$ . Which is the greatest of these integers?

Open in App

Solution

Let $n_{1}$ , $n_{2}$ , $n_{3}$ and $n_{4}$ be four integers in ascending order
Now $\frac{n_{1} + n_{2}}{2} = 102$
$\Rightarrow n_{1} + n_{2} = 204$
and $\frac{n_{1} + n_{2} + n_{3}}{3} = 103$
$\Rightarrow n_{2} + n_{2} + n_{3} = 309$ ---(i)
Also $\frac{n_{1} + n_{2} + n_{3} + n_{4}}{4} = 104$
$\Rightarrow n_{1} + n_{2} + n_{3} + n_{4} = 416$
$\Rightarrow 309 + n_{4} = 416$ (from (i))
$\Rightarrow n_{4} = 416 - 309$
$\Rightarrow n_{4} = 107$
Thus the greatest integer is $107$

Suggest Corrections

Similar questions

Q. The median of 11 different positive integers is 15 and seven of those 11 integers are 8,12, 20, 6, 14, 22 and 13.
I. The difference between the averages of four largest integers and four smallest integers is 13.25.
II. The averages of all 11 integers is 16.
Which of the following statements would be sufficient to find the largest possible integer of these numbers?

Q. The average of four positive integers is 72.5. The highest integer is 117 and the lowest integer is 15. The difference between the remaining two integers is 12. Which is the higher of these two remaining integers?

Q. The average of 9 consecutive positive integers is 63. The product of the largest and smallest integers is

Q. Four positive integers are given. Select any three of these integers, find their arithmetic average, and add this result to the fourth integer. Thus the numbers

29, 23, 21 a n d 17

are obtained. One of the original integers is:

The average of a set of seven consecutive integers is (x + 1) and that of a different set of seven consecutive integers is (x – 1). Find the average of all the integers in both the sets considering all the common integers only once.

Join BYJU'S Learning Program

In a set of four integers, the average of the two smallest integers is 102, the average of the three smallest integers is 103, the average of all four is 104. Which is the greatest of these integers?

Let n1,n2,n3 and n4 be four integers in ascending orderNow n1+n22=102⇒n1+n2=204 and n1+n2+n33=103⇒n2+n2+n3=309 ---(i) Also n1+n2+n3+n44=104⇒n1+n2+n3+n4=416⇒309+n4=416 (from (i))⇒n4=416−309⇒n4=107Thus the greatest integer is 107

In a set of four integers, the average of the two smallest integers is $102$ , the average of the three smallest integers is $103$ , the average of all four is $104$ . Which is the greatest of these integers?