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Average problem. Please help.

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Average problem. Please help.

by aman88 » Wed Dec 12, 2012 3:03 am
Q: Linda purchased 3 books at a book fair. What was the median price of the 3 books?
(1) The average (arithmetic mean) price of the 3 books was $1.5
(2) The price of one of the 3 books was $1.5

IMO E but OA C.

Statement 1 is not enough. Eliminated A and D.
Statement 2 is not enough. Eliminated B.

How are both combined are enough? We only know one of the books is $1.5. How can we find out the median out of this?

Please let me know.

Thanks.
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Source: — Data Sufficiency |
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by sharoonsaleem » Wed Dec 12, 2012 3:20 am
Statement 1

(B1+B2+B3)/3 = 1.5$ ; Not Sufficient

Statement 2

Assume B1 = 1.5$ ; Not Sufficient

Combining them gives:

B1+B2+B3 = 4.5
B2 + B3 = 3
The only arrangement for this to be possible is one book to be greater than 1.5$ and one book to be less than 1.5$, thus 1.5$ is the median.

C is the answer
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by puneetkhurana2000 » Wed Dec 12, 2012 9:27 am
In this question using some numbers can help...

Statement 1 Total is 3*1.5 = 4.5
But individuals can be
1) 1.5, 1.5, 1.5 ...Median 1.5
2) 0.5, 1.0, 3.0 ...Median 1.0

Not Sufficient!!!

Statement 2 One book costs 1.5
We need to have some more information to get the median, so Not Sufficient!!!

Together we get, total = 4.5 and B1 = 1.5

Cases can be
1) 1.5, 1.5, 1.5 ...Median 1.5
2) 1.5, 0.5, 2.5 ...Median 1.5
3) 1.5, 1.0. 2.0 ...Median 1.5

Sufficient!!!

Answer C
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