vinay1983 wrote:If x is an integer and x,5,6,11,19 are a set of numbers, is the median of this set greater than the arithmetic mean of this set?
1. X >= 8
2. X is greater than the median of the 5 numbers
This is a very small twist on this question:
https://www.beatthegmat.com/mean-median-t269562.html
Target question: Is the median greater than the average?
Given: We have the set {x, 5, 6, 11, 19}
Notice that there are 3 possible scenarios we need to consider:
Scenario #1: x is less than 6, in which case the median is 6
Scenario #2: 6
< x
< 11, in which case the median is x
Scenario #3: x is greater than 11, in which case the median is 11
The average of this set will be (41+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 = 9 (median = 9 and average = 10), in which case,
the median is NOT greater than the average
Case b: x = 12 (median = 11 and average = 53/5), in which case,
the median IS 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 = 12 (median = 11 and average = 53/5), in which case,
the median IS greater than the average
Case b: x = 59 (median = 11 and average = 20), 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 = 12 (median = 11 and average = 53/5), in which case,
the median IS greater than the average
Case b: x = 59 (median = 11 and average = 20), 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
