nalinnair
A certain list consists of 400 different numbers. Is the average (arithmetic mean) of the numbers in the list greater than the median of the numbers in the list?
(1) Of the numbers in the list, 280 are less than the average.
(2) Of the numbers in the list, 30 percent are greater than or equal to the average.
Given: A certain list consists of 400 different numbers. Important: If we have an EVEN number of values, then the median = the average of the two middle most values (once the numbers are arranged in ascending order)So, if we arrange all 400 numbers in
ascending order, the median = (the 200th value + the 201st value)/2
Target question: Is the average (arithmetic mean) of the numbers in the list greater than the median of the numbers in the list? Statement 1: Of the numbers in the list, 280 are less than the average. Let's let A = the average of the 400 numbers
So if we arrange all 400 numbers in ascending order, the first 280 numbers are less than A.
This means the 200th value is less than A, and the 201st value is less than A.
If the 200th value and the 201st value are each less than A, then the average of the 200th value and the 201st value must be less than A
In other words, (200th value + 201st value)/2 < A
The answer to the target question is
YES, the average of the numbers IS greater than the median of the numbersSince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: Of the numbers in the list, 30 percent are greater than or equal to the averageThis also tells us that 70% of the numbers are LESS THAN the average.
70% of 400 = 280
So, statement 2 is indirectly telling us that, among the numbers in the list, 280 are less than the average.
In other words, statement 2 is indirectly telling us the SAME THING statement 1 tells us.
Since we already concluded that statement 1 is sufficient, we can also conclude that statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
RELATED VIDEO