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

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Math Expert
Joined: 02 Sep 2009
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Five friends visited a used book store and each friend purchased one  [#permalink]

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02 Aug 2017, 23:50
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Difficulty:

55% (hard)

Question Stats:

49% (01:28) correct 51% (01:28) wrong based on 153 sessions

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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?

A. $15 B.$17
C. $19 D.$21
Since each of the friends need to buy 1 book, and the total cost of the books is 25$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" _________________ You've got what it takes, but it will take everything you've got Intern Joined: 19 Dec 2016 Posts: 45 Location: India Concentration: Technology, Leadership WE: Consulting (Computer Software) Five friends visited a used book store and each friend purchased one [#permalink] ### Show Tags 03 Aug 2017, 01:57 2 i think it is no where mentioned in question that we can't take price in decimal as given lowest price for a book = 1 so 2nd book prices could be 1.01 3rd book prices could be 1.02 4th book prices could be 1.03 5th book price= total price - above four book price =( 25 -(1+1.01+1.02+1.03)) =20.94 when we will round off to nearest integer it will give 21 _________________ If you want to appreciate, just click on Kudos. Manager Joined: 22 Aug 2016 Posts: 80 Location: India Concentration: Operations, Finance GMAT 1: 650 Q49 V29 GMAT 2: 710 Q49 V37 GPA: 3.5 WE: Other (Education) Re: Five friends visited a used book store and each friend purchased one [#permalink] ### Show Tags 03 Aug 2017, 06:30 1 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

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

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03 Aug 2017, 20:11
I doubt that kind of question can be on real GMAT
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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. How about 25 - 20.9 - 1 Manager Joined: 22 Aug 2016 Posts: 80 Location: India Concentration: Operations, Finance GMAT 1: 650 Q49 V29 GMAT 2: 710 Q49 V37 GPA: 3.5 WE: Other (Education) Five friends visited a used book store and each friend purchased one [#permalink] ### Show Tags 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

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

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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?

What am I missing here?
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Re: Five friends visited a used book store and each friend purchased one  [#permalink]

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05 Aug 2017, 14:21
2
1
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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Re: Five friends visited a used book store and each friend purchased one  [#permalink]

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09 Aug 2017, 12:48
1
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 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.

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

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06 Oct 2018, 07:47
1
When you see a Min/Max problem, such as this one that asks you to maximize the value of the highest-priced book, you should always ask yourself:

Quote:
1) Do the values have to be integers?

2) Is zero a possible value?

3) Can the values repeat?

Here you're told that the minimum cost is $1, so zero is not possible. And you're told that the values cannot repeat. But you're not told whether the values have to be integers. Importantly, if neither the text nor the logic of the problem says that the numbers have to be integers, you MUST consider nonintegers! Here you're also given a nice hint: the question says "rounded to the nearest dollar," which is something that you wouldn't normally say unless rounding were a necessary part of the problem. With that in mind, although you cannot repeat values you can certainly make them one penny apart. So to minimize the smallest amounts, you can list them as:$1.00, $1.01,$1.02, and $1.03. This means that the cheapest four books could cost as little as$4.06, meaning that the highest-priced book could cost as much as $20.96, which when rounded to the nearest dollar is$21.

For this reason, choice D is correct.
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Re: Five friends visited a used book store and each friend purchased one   [#permalink] 06 Oct 2018, 07:47
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