The Largest Number
A set of three distinct positive integers has mean 4 and median 5. What is the largest number in the set?
Details and assumptions
The mean of a set of numbers is the average of the set.
The median of a set of numbers is the middle value, which divides the list into two equal halves. If there is an even number of them, the median will be the average of the two middle values.
The answer is 6.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Since the median is 5, it must be one of the numbers in the set. Since the mean is 4, the sum of all the numbers is 3 × 4 = 1 2 . This means that the other two numbers must sum to 1 2 − 5 = 7 . For them to be distinct positive integers, they must be one of { 1 , 6 } , { 2 , 5 } , { 3 , 4 } . However, they cannot be { 2 , 5 } since we already have 5, and they cannot be { 3 , 4 } since 5 is the median. Thus, the other numbers are 1 , 6 and the largest number in the set is 6 .