In a certain set of 300 stocks, each is priced at either $50, $100, or

Question

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 .

KarishmaB · Accepted Answer

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)

sudh · Answer

In a certain set of 300 stocks, each is priced at either $50, $100, or $150.

An investor bought 95 different stocks for 5,000 dollars.
Let  x  be the number of $50 stocks,  y  be $100 stocks, and  z  be $150 stocks
x + y + z = 95

50x + 100y + 150z = 5000
x + 2y + 3z = 100 --> (x + y + z) + y + 2z = 100
y + 2z = 5
since x, y, and z are integers, y could be 1, 3, or 5.
y = 1, z = 2, x = 92 ---(I)
y = 3, z = 1, x = 91 ---(II)
y = 5, z = 0, x = 90 ---(III)

Statement (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.

Case (I) & Case (II)
average price = $100 (average stocks =  \frac{300}{3} )
if average price is $100
 then number of $50 stocks = $150 stocks in order to get average price of 100 and the rest are $100 stocks
  
in either case the 80th percentile (stock #240), when all 300 stocks are ordered by price from least to greatest, is $150

Case (III)
Average price of $150 (average stocks =  \frac{300}{2} ) is not possible with only $50 and $100 stocks

Sufficient

Statement (2)
The mean, median, mode, and range of the 300 stock prices are all identical.

Case (III ),
range (50), median (100), mode (100), and mean (between 50 and 100) contradict each other
so case (III) is not possible

Case (I) & (II) (as above),
range (100)= median (100) = mode (100) = mean (100)

Sufficient

Answer D

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

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.
 
Transforming the original codntiion we have the below table of 2by3 case, expanded from 2by2 case that are common in GMAT tests.

a+b+c=95, 50a+100b+150c=5,000 gives us 3 variables (a,b,c) and 2 equations (a+b+c=95, 50a+100b+150c=5,000). Since we need to match the number of variables and equations, we need 1 more equation and since we have 1 each in 1) and 2), D is likely the answer and it turns out that D actually is the answer.
Remember the three things in solving the question
1-st : the remaining questions * 2 minutes
2-nd : 5 minute deadline
3-rd : not want to solve
and we get D as our answer.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In a certain set of 300 stocks, each is priced at either $50, $100, or

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

In a certain set of 300 stocks, each is priced at either $50, $100, or

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards