x,3,1,12,8
If x is an integer, is the median of the 5 numbers shown greater than the average (AM) of 5 numbers?
1. x >6
2. x is greater than the median of 5 numbers
Target question: Is the median greater than the average?
Given: We have the set {1, 3, 8, 12, x}
Notice that there are 3 possible scenarios we need to consider:
Scenario #1: x is less than 3, in which case the median is 3
Scenario #2: 3
< x
< 8, in which case the median is x
Scenario #3: x is greater than 8, in which case the median is 8
The average of this set will be (24+x)/5.
Okay, now onto the statements
Statement 1: x > 6
This rules our scenario
#1, but we must still consider scenarios
#2 and #3
Here are two possible values of x that yield conflicting answers to the target question:
Case a: x = 7 (median = 7 and average = 31/5), in which case,
the median is greater than the average
Case b: x = 21 (median = 8 and average = 9), in which case,
the median is NOT greater than the average
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x is greater than the median of the 5 numbers
This rules our scenarios
#1 and #2, which leaves scenario
#3
Here are two possible values of x that yield conflicting answers to the target question:
Case a: x = 11 (median = 8 and average = 7), in which case,
the median is greater than the average
Case b: x = 21 (median = 8 and average = 9), in which case,
the median is NOT greater than the average
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that the x-values we used to show that statement 2 is not sufficient ALSO satisfy statement 1. So, we know immediately that the combined statements are NOT SUFFICIENT.
To see what I mean, here are the two conflicting cases:
Case a: x = 11 (median = 8 and average = 7), in which case,
the median is greater than the average
Case b: x = 21 (median = 8 and average = 9), in which case,
the median is NOT greater than the average
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT.
Answer =
E
Cheers,
Brent
