Question

A list of 5 positive integers has all of the following properties:______.

• the only integer in the list that occurs more than once is 8,
• its median is 9, and
• its average (mean) is 10.
What is the largest possible integer that could appear in the list?
(Note: The median of a set of five positive integers is the middle integer when the
set is arranged in increasing order.)
(A) 15
(B) 16
(C) 17
(D) 24
(E) 25

Answer 1

The correct option is;

(B) 16

Explanation:

There are 5 integers with the number 8 occurring more than once

The median = 9

The mean = 10

When we arrange the integers in increasing order we have

A + B + C + D + E

There are at lest two 8s, with the median = 9

Therefore, we have

A, 8, 8, D, E

The average is 10, and since we have 5 positive integers, therefore

Average = ∑x/n

Where:

n = Count of numbers = 5

∑x = Sum of the 5 numbers

∑x/5 = 10

∴ ∑x = 50

or A + 8 + 8 + D + E = 50

or 8 + 8 + 9 + D + E = 50

D + E = 25

or 8 + 8 + 9 + 9 + 16 = 50 since the median can be gotten at the middle

Therefore, the largest possible integer that could appear on the list = 16.

Answer 2

(A) 15

Explanation:

(1) There are 5 integers; in order they are A, B, C, D, and E.

(2) The median is 9: A, B, 9, D, E

(3) 8 is the only number that occurs more than once: 8, 8, 9, D, E

(4) The mean is 10: (8+8+9+D+E)/5 = 10 --> D+E = 25

The largest possible value for E is when D is as small as possible. Since only 8 occurs more than once, D should be 10; that makes E 15.

ANSWER: 15