The range of the six numbers 20, 6, 14, 8, 28, and K is 24. The greate

Question

The range of the six numbers 20, 6, 14, 8, 28, and K is 24. The greatest possible value of K is how much greater than the least possible value of K?

(A) 4
(B) 24
(C) 26
(D) 30
(E) 34

Hatakekakashi · Answer

6,8,14,20,28,k

range = 24

30-6=24
28-4=24

k can be 4/30
difference

26

US09 · Answer

C.

Greatest possible value of K = 30
Least possible value of K = 4
Difference = 26.

ScottTargetTestPrep · Answer

The greatest value of K is 6 + 24 = 30

The least value of K is 28 - 24 = 4.

So the difference between those numbers is 30 - 4 = 26.

Alternate Solution:

Recall that range = largest - smallest.

If K is to be as large as possible, it is the largest of the 6 values in the set, and so the range of the data would be K - 6 = 24, so K = 30.

If K is to be as small as possible, it is the smallest of the 6 values in the set, so the range of the data is 28 - K = 24, so K = 4.

The difference in the two values of K is 30 - 4 = 26.

Answer: C

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