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?

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Solution

Let the integers be $l, m, n, o$ in which $(l > m > n > o)$

Now, $\frac{n + o}{2} = 102 \Rightarrow n + o = 204............. (1) \frac{m + n + o}{3} = 103 \Rightarrow m + n + o = 309............ (2)$

Again, $\frac{l + m + n + o}{4} = 104 \Rightarrow l + m + n + o = 416.......... (3)$

Subtracting (2) from (3)
$l = 416 - 309 = 107$

Hence, $107$ is the greatest Number

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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 the integers be l,m,n,o in which (l>m>n>o)Now, n+o2=102⇒n+o=204.............(1)m+n+o3=103⇒m+n+o=309............(2)Again, l+m+n+o4=104⇒l+m+n+o=416..........(3)Subtracting (2) from (3)l=416−309=107Hence, 107 is the greatest Number