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Set X has 5 numbers, whose average is greater than their
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11 Mar 2008, 12:32
Set X has 5 numbers, whose average is greater than their median. Set Y has 7 numbers, whose average is also greater than their median. If the 2 sets have no number in common and are combined to a new set, is the average of the new set greater than its median?
(1) The average of Y is greater than the average of X. (2) The median of Y is greater than the median of X.
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Re: Set X has 5 numbers, whose average is greater than their
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16 Mar 2008, 21:23
I am guessing it's C because question includes reference to both median and average, but couldn't comeup with a logical way to tackle it. will wait for someone to elighten me!
Re: Set X has 5 numbers, whose average is greater than their
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17 Mar 2008, 00:31
sreehari wrote:
I am guessing it's C because question includes reference to both median and average, but couldn't comeup with a logical way to tackle it. will wait for someone to elighten me!
OA is E. anyway, how to tackle this type of ds statistics problem in just 2 minutes?
Re: Set X has 5 numbers, whose average is greater than their
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17 Mar 2008, 06:19
walker wrote:
Tough one... I think the fastest way to solve the problem - try to construct examples.
1) 0--XXMAX-------------------------------------------------------------------YYYMAYY Median of a new set is greater than average.
2) 0--XXMAX-- 0---YYYMAYY
Median of a new set is smaller than average.
hope not to find questions like this in the actual test
anyway, this could be an explanation:
(1) y > x. We know that the average of the elements in X U Y is between x and y. We can say that at least three of the elements of X are less than this average. If one element in Y is very large, it could be that all other elements of Y are less than this average, so However, if all elements of Y are nearly same, all will be above this average. For example, suppose x=3 , y=5 and X = { 2,2,2,2,7} . If Y= {3,3,3, ... , 3 , 17} . The average of the combined set X U Y is greater than 4, but the median is 4. Conversely, if Y= {4.9, 4.9,4.9,...,4,9, 5.6}, the median, 4.9 is greater than the mean of X U Y. NOT SUFF. (2) Since the median of X is less than the median of Y, the median of X U Y will be less than the median of Y, but greater than the median of X. Without information about the averages of the elements in X and those in Y, we cannot answer the question. In each of the two examples cited in (1), the median of X is less than the median of Y. NOT SUFF (T) NOT SUFF
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Thank you for understanding, and happy exploring!
gmatclubot
Re: Set X has 5 numbers, whose average is greater than their [#permalink]