Bunuel wrote:
In a certain set of 300 stocks, each is priced at either $50, $100, or $150. If an investor bought 95 different stocks for 5,000 dollars, what was the price of the stock in the 80th percentile, when all 300 stocks are ordered by price from least to greatest?
(1) The average price of the 300 stocks is the same as the average number of stocks in the set of 300 that have each price.
(2) The mean, median, mode, and range of the 300 stock prices are all identical.
Kudos for a correct solution.
Total number of stocks = 300
Price of each = $50/$100/$150
"If an investor bought 95 different stocks for 5,000 dollars" - Think about this a bit before you move on.
95 is close to 100 and if the investor had bought 100 stocks for $5000, his average price each stock would have been $50. So mostly, he bought the cheapest stocks. So most of the 95 stocks would be $50 stocks.
80th percentile of 300 is (80/100)*300 = 240. So the price of the 240th stock will lie in the 80th percentile. We need to know this price.
(1) The average price of the 300 stocks is the same as the average number of stocks in the set of 300 that have each price.
Average price of 300 stocks = Average number of stocks of each price
Let's calculate "Average number of stocks of each price"
The sum of the number of stocks = 300
The total different prices = 3
Average number of stocks of each price = 300/3 = 100
So average price of 300 stocks = $100
If we have at least about 90 $50 stocks, we must have at least about 90 $150 stocks too to balance out the deficit. So the 240th stock will be $150 stock.
Sufficient alone.
(2) The mean, median, mode, and range of the 300 stock prices are all identical.
Range 0 if all stocks are of the same price: Range cannot be 0 since the mean price cannot be 0.
Range 50 if all stocks are of '$50 and $100' (or '$100 and $150'): Range cannot be 50 since mean price cannot be 50 if there are some $100 stocks too.
So Range must be 100 and there must be stocks of all 3 prices.
This means average price of the stocks = $100
If we have at least about 90 $50 stocks, we must have at least about 90 $150 stocks too to balance out the deficit. So the 240th stock will be $150 stock.
Sufficient alone.
Answer (D)
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >