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Median/Mean Question

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Median/Mean Question

by sharoonsaleem » Wed Dec 12, 2012 3:34 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

The answer is (C)

First statement is insufficient, second is also insufficient.
If i was to combine both:

(B1+B2+B3)/3 = 1.5

if B1 = 1.5 $

Then: B2+B3+1.5 = (1.5*3)

B2+B3 = 3

How do we get that median is 1.5$ from this...??
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Source: — Data Sufficiency |
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by David Mahler » Wed Dec 12, 2012 7:43 am
If one of the books cost $1.50, and the other two combined cost $3.00, try different values for B2 and B3 and see what the median is in each case:

B1 = $1.50, B2 = $1.50, B3 = $1.50 median = $1.50
B1 = $1.50, B2 = $1.00, B3 = $2.00 median = $1.50
B1 = $1.50, B2 = $0.01, B3 = $2.99 median = $1.50

No matter what values you choose for B2 and B3, either all 3 books cost $1.50, or one value is less than $1.50 and 1 value is greater than $1.50. Either way, the median is always $1.50
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by GMATGuruNY » Wed Dec 12, 2012 7:49 am
sharoonsaleem wrote: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
Statement 1: The average (arithmetic mean) price of the 3 books was $1.5.
Sum = 3(1.5) = 4.5.
Case 1: The 3 prices are {1.5, 1.5, 1.5}, in which case the median is 1.5.
Case 2: The 3 prices are {.5, 2, 2}, in which case the median is 2.
INSUFFICIENT.

Statement 2: The price of one of the 3 books was $1.5.
Case 1: The 3 prices are {1.5, 1.5, 1.5}, in which case the median is 1.5.
Case 2: The 3 prices are {1.5, 100, 100}, in which case the median is 100.
INSUFFICIENT.

Statements combined:
Both statements are satisfied by {1.5, 1.5, 1.5}, in which case the median is 1.5.

If the value in red DECREASES, the value in blue must INCREASE, so that the sum remains 4.5:
{1, 1.5, 2}.
The result is that the median remains 1.5.

If the value in red INCREASES, the value in blue must DECREASE, so that the sum remains 4.5:
{2.5, 1,5, .5}, which in ascending order becomes {.5, 1.5, 2.5}
The result is that the median remains 1.5.

Since the median will be 1.5 in every case, SUFFICIENT.

The correct answer is C.
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