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Five friends visited a used book store and each friend purchased one book. No two friends paid the same amount for a book, and the lowest book price was $1. If the sum of all book prices was $25, what is the maximum price that any one book cost, rounded to the nearest dollar?

Five friends visited a used book store and each friend purchased one [#permalink]

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03 Aug 2017, 00:21

The minimum price per book is 1$. Since each of the friends need to buy 1 book, and the total cost of the books is 25$ the costliest book that could be bought is 21$(since the other books are bought at 1$ each)

Hence, Option D is the correct answer!

P.S It is very easy to mistake "No two friends paid the same amount for a book" to mean "no two friends bought a book for the same price"
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03 Aug 2017, 06:30

1

This post received KUDOS

Bunuel wrote:

Five friends visited a used book store and each friend purchased one book. No two friends paid the same amount for a book, and the lowest book price was $1. If the sum of all book prices was $25, what is the maximum price that any one book cost, rounded to the nearest dollar?

A. $15 B. $17 C. $19 D. $21 E. $23

The better approach would be to start with the options. (E)Let us say the rate for the costliest book is 23. We know the least book's price is 1 and total is 25. So the sum of the costs of other 3 books will be (25-23-1) = 1 This is not an acceptable value for the sum of 3 books since we already know that the least book's price is 1.

(D)If the rate for the costliest book is 21, sum of the costs of other 3 books will be (25-21-1)=3 This is also not possible. If sum of costs=3, maximum possible case for the cost of each book is \(\frac{3}{3}\)=1 However since the cost of each book is distinct, this is also not possible.

(C)If the rate for the costliest book is 21, sum of the costs of other 3 books will be (25-1-19) = 5. Each book can have a different value if the sum of the 3 books is 5 and the condition of least value being 1 can be maintained. So the maximum cost possible is 19.

Re: Five friends visited a used book store and each friend purchased one [#permalink]

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03 Aug 2017, 19:36

I can't wait to see the answer.. There are several answer here.. I want to know which one is right Myself calculate the questions by assuming cost of each book is in integer

Re: Five friends visited a used book store and each friend purchased one [#permalink]

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03 Aug 2017, 21:06

sarathgopinath wrote:

Bunuel wrote:

Five friends visited a used book store and each friend purchased one book. No two friends paid the same amount for a book, and the lowest book price was $1. If the sum of all book prices was $25, what is the maximum price that any one book cost, rounded to the nearest dollar?

A. $15 B. $17 C. $19 D. $21 E. $23

The better approach would be to start with the options. (E)Let us say the rate for the costliest book is 23. We know the least book's price is 1 and total is 25. So the sum of the costs of other 3 books will be (25-23-1) = 1 This is not an acceptable value for the sum of 3 books since we already know that the least book's price is 1.

(D)If the rate for the costliest book is 21, sum of the costs of other 3 books will be (25-21-1)=3 This is also not possible. If sum of costs=3, maximum possible case for the cost of each book is \(\frac{3}{3}\)=1 However since the cost of each book is distinct, this is also not possible.

(C)If the rate for the costliest book is 21, sum of the costs of other 3 books will be (25-1-19) = 5. Each book can have a different value if the sum of the 3 books is 5 and the condition of least value being 1 can be maintained. So the maximum cost possible is 19.

Five friends visited a used book store and each friend purchased one [#permalink]

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03 Aug 2017, 21:43

pradeepmaria wrote:

sarathgopinath wrote:

Bunuel wrote:

Five friends visited a used book store and each friend purchased one book. No two friends paid the same amount for a book, and the lowest book price was $1. If the sum of all book prices was $25, what is the maximum price that any one book cost, rounded to the nearest dollar?

A. $15 B. $17 C. $19 D. $21 E. $23

The better approach would be to start with the options. (E)Let us say the rate for the costliest book is 23. We know the least book's price is 1 and total is 25. So the sum of the costs of other 3 books will be (25-23-1) = 1 This is not an acceptable value for the sum of 3 books since we already know that the least book's price is 1.

(D)If the rate for the costliest book is 21, sum of the costs of other 3 books will be (25-21-1)=3 This is also not possible. If sum of costs=3, maximum possible case for the cost of each book is \(\frac{3}{3}\)=1 However since the cost of each book is distinct, this is also not possible.

(C)If the rate for the costliest book is 21, sum of the costs of other 3 books will be (25-1-19) = 5. Each book can have a different value if the sum of the 3 books is 5 and the condition of least value being 1 can be maintained. So the maximum cost possible is 19.

How about 25 - 20.9 - 1

Yes, 20.9 is possible and the question asks you to round it to the closest value. But the closer value being 21, which is not an acceptable value, I don't think we can do that. Again, this is what I think is true. May be you are right. The closest possible value of 20.9 should be 20, which is not there in options. Next possible closest value is 19.

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05 Aug 2017, 13:19

pushpitkc wrote:

The minimum price per book is 1$. Since each of the friends need to buy 1 book, and the total cost of the books is 25$ the costliest book that could be bought is 21$(since the other books are bought at 1$ each)

Hence, Option D is the correct answer!

P.S It is very easy to mistake "No two friends paid the same amount for a book" to mean "no two friends bought a book for the same price"

Take the essence of each of your sentences and write each sentence in the corresponding singular affirmative case (where each of four friends A, B, C, and D parts with one dollar for one book):

"No two friends paid the same amount for a book." A paid the amount of $1 for a book. B paid the amount of $1 for a book. C paid the amount of $1 for a book. D paid the amount of $1 for a book.

It appears to me that A and B paid the same amount, as did A and C, A and D, B and C, B and D, and C and D. There are six cases that seem to defy the rule that "No two friends paid the same amount for a book."

Do you mean that the sentence suggests that three and/or four friends can pay the same amount, but not "just" two?

The other sentence: "No two friends bought a book for the same price."

A bought the book for the price of $1.00 B bought the book for the price of $1.00 C bought the book for the price of $1.00 D bought the book for the price of $1.00

I see neither the logical difference between the two sets of sentences nor the difference between their corresponding antecedent sentences.

If you are distinguishing between "paid [an] amount for," and "bought for [a] price of," what is the distinction?

I believe that "No two friends paid the same amount for a book" means the same thing as "no two friends bought a book for the same price". Both of these phrases mean that there were no duplicate prices, that is, all five of the friends paid unique amounts for their books.

Assuming that this is what the problem writer intended, I agree with the decimal solution above. The first four books were $1.00, $1.01, $1.02, and $1.03. That leaves $20.94 for the final book, or approximately $21.
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Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

Five friends visited a used book store and each friend purchased one book. No two friends paid the same amount for a book, and the lowest book price was $1. If the sum of all book prices was $25, what is the maximum price that any one book cost, rounded to the nearest dollar?

A. $15 B. $17 C. $19 D. $21 E. $23

The least amount of money that 4 of the friends could have paid was $1, $1.01, $1.02, and $1.03. Thus, the maximum the last friend would have paid is 25 - (1 + 1.01 + 1.02 + 1.03) = 25 - 4.06 = 20.94 ≈ $21.

Answer: D
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