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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