A book dealer buys used books for prices ranging from $0.75 to $1.50

Question

A book dealer buys used books for prices ranging from $0.75 to $1.50 and then sells them for prices ranging from $3.00 to $5.50. If the dealer were to sell 20 of these books, the minimum gross profit from this sale would be

A. $15
B. $30
C. $45
D. $50
E. $80

A. $15
B. $30
C. $45
D. $50
E. $80

PS21158

BrentGMATPrepNow · Accepted Answer

Profit = (sale price) - (original purchase price)

In order to MINIMIZE the profit, we must MAXIMIZE the original purchase price, and MINIMIZE the sale price.

MAXIMIZE the original purchase price 
The original purchase price ranges from $0.75 to $1.50
So the MAXIMUM original purchase price (per book) =  $1.50

MINIMIZE the sale price 
The sale price ranges from $3.00 to $5.50
So the MINIMUM sale price (per book) =  $3.00

So the minimum profit (per book) =  $3.00  -  $1.50  =   $1.50

If the dealer were to sell 20 of these books, the minimum gross profit from this sale would be  
If the minimum profit (per ONE book) =   $1.50  
Then the minimum profit for TWENTY books = (20)(  $1.50  ) =  $30

Answer: B

Cheers, 
Brent

GMATinsight · Answer

profit = sale price - cost

Minimum Gross Profit will be obtained when cost is highest and sale price is lowest

Let, cost of all = 1.5
Sale price of all = 3

Minimum Gross profit on one book = 3-1.5

Minimum Gross profit on 20 book s= 20*1.5 = 30

Answer: Option B

yashikaaggarwal · Answer

Minimum Gross Profit is When the Cost Price is maximum and selling price is minimum.
The maximum cost price at which he can purchase a book = $1.5/book

The minimum selling price at which he can sell book is = $3/book

S.P. - C.P. = Profit
20(3)-20(1.5)
60-30
30$..
Answer is B

Posted from my mobile device

Abhishek009 · Answer

GP_{Min} = SP_{Min} - CP_{Max}

Or,  GP_{Min} = 20 ( 3.00 - 1.50 )

Or,  GP_{Min} = 30 , Answer must be (B)

NitishJain · Answer

Minimum profit when bought at the highest possible price and sold at a minimum price.

Minimum profit when all 20 books were bought at $1.50 and sold at $3.00 i.e. profit on each book will be $1.50 ($3.00 - $1.50).

Profit = 20 * 1.50 = $30.

B.

ScottTargetTestPrep · Answer

The minimum profit for each book occurs when he sells the $1.50 (cost) books for $3.00 each, making $1.50 on each book. Thus, the minimum gross profit for selling 20 such books is 20 x $1.50 = $30.

Answer: B

gmatway · Answer

Everyone is trying the typical method . Lately I discovered this new approach as I always get confused in min max calc I have turned these questions into min distance and max distance on NUMBER LINE .

we know profit = S.P - C.P so lets draw these values on number line 
 .75(CP)____1.50 (CP)___________3(sp)_________5.50(sp) Now to ensure minimum profit we can try minimise the distance between CP and SP . In other words we want to maximise the CP and minimize the SP .
Hence 20 (1.50 -3) = 30$

DanTheGMATMan · Answer

Optimize for the lowest profit per book (highest cost and lowest sell price), and multiply by 20:

https://www.youtube.com/watch?v=mhVrfKR81vo

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.

A book dealer buys used books for prices ranging from $0.75 to $1.50

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 Problem Solving (PS) Questions

A book dealer buys used books for prices ranging from $0.75 to $1.50

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