The median of the list of positive integers above is 5.5

Question

8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list?

A. 3
B. 5.5
C. 6.25
D. 7
E. 7.5

Bunuel · Accepted Answer

8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list? 
A. 3
B. 5.5
C. 6.25
D. 7
E. 7.5

Notice that we are told that x is a positive integer.

The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.

Since given that the median is 5.5 (the average of 5 and 6) then integer x must be less than or equal to 5, in order 5 and 6 to be two middle numbers. So our list in ascending order is: {x, 5, 6, 8}. Now, since  x\leq{5}  then the maximum sum of the numbers is 5+5+6+8=24, so the maximum average is 24/4=6 (options C, D, and E are out). 3 cannot be the average because in this case the sum of the numbers must be 4*3=12, which is less than the sum of just two numbers 6 and 8 (remember here that since x is a positive integer it cannot decrease the sum to 12). So we are left only with option B (for x=3 the average is (3+5+6+8)/4=22/4=5.5).

Answer: B.

piyatiwari · Answer

Given "The median of the list of positive integers above is 5.5"

So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 5.5

so the sequence will be x 5 6 8

Lets say x = 4, which gives us mean = sum/4 = 5.5

B is correct

Sachin9 · Answer

This is amazing soln
I solved by plugging in..

(8+5+x+6)/4 . .
plug nos from options 1 by 1..

when ans 5.5 is plugged in,you get x=3. .
so you have 3,5,6,8 as the order which confirms with the given data :lol:

Zarrolou · Answer

8, 5, x, 6

The median of the list of positive integers above is 5.5. Which of the following could be the average (arithmetic mean) of the list?

If the median is 5.5, then x cannot be >8 ( 5,6,8,9 median 7>5,5). It cannot be > 6 (5,6,7,8 median 6.5>5.5).
So we have found that  x<=5

\frac{x+5+6+8}{4}=mean 
 x=mean*4-19 
x is an integer so 4*mean - 19 must be an integer, option (C)6.25 is out.
(D)7 (E)7.5 these options return values of x > 9, so they cannot be right.
Option (A)3 returns a negative integer, but x must be positive.
Option (B)5.5 is correct, and the value of x is 3, which is possible given the initial condition of "The median of the list of positive integers above is 5.5"

anbuKp · Answer

The median is above 5.5, shouldn't we consider options like x,5,6,8 & 5,6,8,x & 5,6,x,8 ?

What Am I missing?

Bunuel · Answer

The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order. So, if the set in ascending order is {5, 6, x, 8} (meaning if 6\leq x \leq 8 ), then the median would be the average of 6 and x, and it cannot be 5.5, it could be at least 6, for x = 6. Similarly if if the set in ascending order is {5, 6, 8, x} (meaning if x \geq 8 ), then the median would be the average of 6 and 8, so 7, not 5.5. Thus, since given that the median is 5.5 (the average of 5 and 6) then integer x must be less than or equal to 5, in order 5 and 6 to be two middle numbers. So our list in ascending order is: {x, 5, 6, 8}. Check complete solution here: https://gmatclub.com/forum/the-median-o ... l#p1064955 Hope it helps.

ScottTargetTestPrep · Answer

Solution:

Since the median is 5.5, which is (5 + 6)/2, we see that x must be the smallest number in the list, i.e., x ≤ 5. However, we are also given that x is a positive integer, so x ≥ 1. We can create the following inequality for the average:

(1 + 5 + 6 + 8)/4 ≤ (x + 5 + 6 + 8)/4 ≤ (5 + 5 + 6 + 8)/4

5 ≤ (x + 5 + 6 + 8)/4 ≤ 6

Since only 5.5 is between 5 and 6, we see that choice B is the correct answer.

Answer: B

ashKing12 · Answer

0\leq{x}\leq{5}

adding 19 both side

0+19\leq {x+19}\leq{5+19}

dividing by 4 both sides

\frac{19}{4}\leq{\frac{(x+19)}{4}}\leq{\frac{24}{4}}

4.7\leq{mean}\leq{6}

option B

The median of the list of positive integers above is 5.5

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The median of the list of positive integers above is 5.5

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