Statistics - Median and Range Combination Question

SampathKp wrote: ↑

Fri Dec 20, 2019 3:27 am

For 11 distinct positive integers , Median is 90 and Range is 60. Median of the 5 smallest integers is 65. What is maximum range of 5 largest integers

A. 60
B 35
C 32
D 65
E Cant be computed
[/spoiler]

Say the first five integers are x, y, z, p and q; thus, z = 65 (Median - given); Again, say the greatest five integers are r, s, t, u and v; thus, v = x + 60 (given that range is 60). Since there are 11 integers, the 6th integer would be median = 90.

So, the 11 integers are:

x, y, 65, p, q, 90, r, s, t, u, (x + 60)

We have to find out the maximum possible range of r, s, t, u, (x + 60). Or, the maximum possible value of x + 60 – r.

To get the maximum possible value of x + 60 – r, we must maximize x and minimize r. The maximum possible value of x = 63 (= 65 – 1 – 1) and the minimum possible value of r = 91 (= 90 + 1) (Note that the integers are distinct.)

Thus, the maximum possible value of x + 60 – r = 63 + 60 – 91 = 32.

The correct answer: C

Hope this helps!

-Jay
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