mean and median

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cypherskull: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sat Mar 31, 2012 3:39 am; Location: Calcutta; Thanked: 8 times

mean and median

by cypherskull » Fri Aug 24, 2012 10:55 am

Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?

(1) The mean of Set A is greater than the median of Set B.

(2) The median of Set A is greater than the median of Set C.

OA: E

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 24, 2012 10:55 am

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Fri Aug 24, 2012 6:52 pm

cypherskull wrote:Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?

(1) The mean of Set A is greater than the median of Set B.

(2) The median of Set A is greater than the median of Set C.

OA: E

the first answer which comes to my mind is e as st(1) is devoid of any sense mean vs. median and the second statement taken alone is tempting to imply middle of set A increased because of middle in set B which must be greater. But then how we know if the middle of set A isn't greater than the middle of set B too? Tow statements taken together also do not suffice for making right decision.

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by Brent@GMATPrepNow » Sat Aug 25, 2012 8:02 am

cypherskull wrote:Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?

(1) The mean of Set A is greater than the median of Set B.

(2) The median of Set A is greater than the median of Set C.

Tricky!

Target question: Is the median of Set B greater than the median of Set A?

Once we have a hunch that the statements might not be sufficient, we can start looking for conflicting cases.

Let's jump right to . . .

Statements 1 + 2 combined:
Given the information, many different cases are possible. Here are two:

case a:
Set A: 1, 2, 5, 100 (mean = 27, median = 3.5)
Set B: (median = 5)
Set C: 1, 2, 100 (median = 2)
In this case, the median of Set B IS greater than the median of Set A?

case b:
Set A: 1, 3, 7, 7, 100 (mean = 24, median = 7)
Set B: 7, 7 (median = 7)
Set C: 1, 3, 100 (median = 3)
In this case, the median of Set B IS NOT greater than the median of Set A?

Since we can't answer the target question with certainty, the combined statements are NOT SUFFICIENT, so the answer is E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com