Statistics - Median and Range Combination Question

[SampathKp]

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]

[Jay@ManhattanReview]

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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[shekki]

Suppose there are 11 blanks
_ _ _ _ _ _ _ _ _ _
Median is 90 so middle number is 90.
Also median of smallest 5 numbers is 65.
They can be filled as :
_ _ 65 _ 90 _ _ _ _ _
Now for max range, the first number has to be minimum possible, the number immediately after 90 should be minimum possible and the last number should be maximum possible.
So they can be filled as
63 _ 65 _ 90 91 _ _ _ _
Since range = 60, the last number should be 63+60 = 123
Hence range of biggest 5 digit numbers is = 123-91 = 32
So ans is C