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Mean-Median

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Mean-Median

by Anindya Madhudor » Sat Dec 01, 2012 8:54 pm
Set A, Set B, 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?

i. The mean of Set A is greater than the median of Set B.
ii. The median of Set A is greater than the median of Set C.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun Dec 02, 2012 7:58 am
Anindya Madhudor wrote:Set A, Set B, 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?

i. The mean of Set A is greater than the median of Set B.
ii. 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
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