If a set of numbers consists of \(10, 15, 0, 3,\) and \(x,\) and the range of the set is \(30,\) what are the possible

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If a set of numbers consists of \(10, 15, 0, 3,\) and \(x,\) and the range of the set is \(30,\) what are the possible values for the median of the set?

A. -15 and 30
B. 15 and 10
C. 0 and 3
D. 3 and 15
E. 3 and 10

Answer: E

Source: Princeton Review
Source: — Problem Solving |

Junior | Next Rank: 30 Posts
Posts: 15
Joined: Sat Sep 12, 2020 8:07 pm
The range is the difference b/w smallest and the largest values of the set.

To make the range 30, x could take only 2 values
-45 or 30

The median is the middlemost value of the set when the numbers are arranged in ascending (or descending) order. Arranging the constants in ascending order,

We get 0,3,10,15

now if x is -45, the median is 3
and if x is +30, the median is 10

so median could be any of 3 and 10

Correct answer is E

Junior | Next Rank: 30 Posts
Posts: 15
Joined: Sat Sep 12, 2020 8:07 pm
The range is the difference b/w smallest and the largest values of the set.

To make the range 30, x could take only 2 values
-45 or 30

The median is the middlemost value of the set when the numbers are arranged in ascending (or descending) order. Arranging the constants in ascending order,

We get 0,3,10,15

now if x is -45, the median is 3
and if x is +30, the median is 10

so median could be any of 3 and 10

Correct answer is E