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

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Bunuel
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A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   22 May 2020, 08:38
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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


PS21158
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B
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BrentGMATPrepNow
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Re: A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   24 May 2020, 09:06
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Bunuel wrote:
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
PS21158


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

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Brent
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A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   22 May 2020, 08:42
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Bunuel wrote:
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


PS21158


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
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Re: A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   22 May 2020, 08:43
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

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A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   22 May 2020, 08:45
Bunuel wrote:
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


PS21158

\(GP_{Min} = SP_{Min} - CP_{Max}\)

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

Or, \(GP_{Min} = 30\), Answer must be (B)
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Re: A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   24 May 2020, 14:13
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.
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Re: A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   31 May 2020, 04:11
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Bunuel wrote:
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




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
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Re: A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   17 Jul 2020, 04:09
Bunuel wrote:
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


PS21158


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$
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Re: A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink] New post   25 Oct 2022, 02:25
Hello from the GMAT Club BumpBot!

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Re: A book dealer buys used books for prices ranging from $0.75 to $1.50 [#permalink]
25 Oct 2022, 02:25
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