Question

The penguins currently living on an island are of two types, Chinstrap penguins and Gentoo penguins. The range of the heights of the Chinstrap penguins on the island is 13.2 centimeters, and the range of the heights of the Gentoo penguins on the island is 15.4 centimeters.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the penguins on the island?

Indicate all such statements.

A The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
B The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.
C The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.

Correct Answer: A

-PLEASE GIVE STEP BY STEP THOROUGH EXPLANATION...HAVING A HARD TIME WITH THIS QUESTION!

Answer 1

The range is the difference between the maximum and minimum value.

The range for chinstrap penguins -

R(c) = Max(c) - Min(c) = 13.2

The range for Gentoo penguins -

R(g) = Max(g) - Min(g) = 15.4

A.

Max(c) = x

Max(g) = x + 5.8

R(c) = x - Min(c) = 13.2 ---> x = 13.2 + Min(c)

R(g) = x + 5.8 - Min(g) = 15.4 ---> x = 9.6 + Min(g)

equate both of them

13.2 + Min(c) = 9.6 + Min(g)

Min(g) - Min(c) = 3.6

It means Min(c) is less than the Min(g) whereas Max(g) is greater than Max(c).

So, for all the penguins, the Max will be taken for g and the minimum will be taken for c.

Range(all penguins) = Max(g) - Min(c) = x + 5.8 - x + 13.2 = 19

Hence, it can be determined with this option.

B.

The median height can't help in calculating the range.

C.

The relation between average height can't be sued to calculate the range.

Option A is the right answer.