wunsun wrote:
List P contains m numbers; list Q contains n numbers. If the two lists are combined to produce list R, containing m + n numbers, is the median of list R greater than the median of list P ?
(1) The smallest number in list Q is greater than the largest number in list P.
(2) m = n
Need some help; see spoiler below.
I got this questions wrong since it was not defined that the any of the numbers are positive, i.e. if the set of n number are negative, then m+n < m, therefore the median of list R is less than the median of list P. However, it if is positive, then median of list R is greater than the median of list P.
Is the word number stating that it is the set of natural numbers?
I picked E
Source
MGMAT CAT.
Before looking at the statements, it is important to remember that nothing in the question assumes that the numbers in either list must all be different. For instance, if list P contains 3 numbers, {1, 2, 3} is one possible set, as is {1, 1, 1}.
(1): INSUFFICIENT. Under this condition, it is possible for the median of the combined list R to be greater than the median of set P. For instance, if list P contains the numbers 1, 2, and 3, and list Q contains the numbers 4, 5, and 6, then the median of list R (which contains all six numbers) is 3.5, which is greater than 2 (the median of list P).
It is also possible for the median of the combined set to equal the median of list P. For instance, if list P contains the numbers 1, 1, 1, and 1, and list Q contains the numbers 2, 2, and 2, then the median of list P is 1, and the median of list R is also 1.
(2): INSUFFICIENT. This information does not tell us whether the median of list R is greater than the median of list P. For instance, if list P contains the numbers 1, 2, and 3, and list Q contains the numbers 4, 5, and 6, then the median of list R (which contains all six numbers) is 3.5, which is greater than 2 (the median of list P).
It is also possible for the median of the combined set to equal the median of list P, as is perhaps most easily seen in cases in which all of the numbers are the same: e.g., if list P contains 1, 1, and 1, as does list Q, then the median of all three lists P, Q, and R is 1.
(1) AND (2): SUFFICIENT. If both conditions are true, then the set will have two middle values: the largest value in list P and the smallest value in list Q. According to statement (1), these values are different, so the median, found by averaging them, will be distinct from both; the median will be greater than the value from list P, and less than the one from list Q. Since the median is greater than the largest value in list P, it must be greater than every value in list P, and so greater than the median of P; therefore, this statement is sufficient.
The correct answer is C.