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A bookstore that sells used books sells each of its paperbac

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?

(1) Joe bought 2 paperback books and 3 hardcover books for $12.50.
(2) Paul bought 4 paperback books and 6 hardcover books for $25.00.

Data Sufficiency
Question: 108
Category: Algebra Applied problems
Page: 161
Difficulty: 650


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Re: A bookstore that sells used books sells each of its paperbac [#permalink]

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New post 23 Feb 2014, 07:48
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SOLUTION

A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?

We should find the value of p+h, where p is the price of one paperback and h is the price of one hard cover book.

(1) Joe bought 2 paperback books and 3 hardcover books for $12.50 --> 2p + 3h = 12.5. Not sufficient.

(2) Paul bought 4 paperback books and 6 hardcover books for $25.00 --> 4p + 6h = 25. Not sufficient.

(1)+(2) We can get 4p + 6h = 25 by multiplying 2p + 3h = 12.5 by 2, thus even when combining the statements we still have only one equation. Not sufficient.

Answer: E.
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Re: A bookstore that sells used books sells each of its paperbac [#permalink]

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New post 24 Feb 2014, 00:27
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A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?

(1) Joe bought 2 paperback books and 3 hardcover books for $12.50.
(2) Paul bought 4 paperback books and 6 hardcover books for $25.00.



Sol: Let the price of paperbook be "X" and that of Hardcover be "Y". So we need to find X+Y?

St 1: 2X+3Y=12.5. There are multiple values possible so not sufficient.
A and D ruled out

St 2: 4X+6Y=25 or 2X+3Y=12.5 which is same information as St 1 So B ruled out

Combining the 2 statements, we get no new information so ans is E.

650 level is okay
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Re: A bookstore that sells used books sells each of its paperbac [#permalink]

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New post 24 Feb 2014, 03:48
Option E.
From S1:Let price per paperback=x &
price per hardcover=y
2x+3y=12.50.Not suff since two variables,one equation can't be solved.

From S2:4x+6y=25
Nothing but 2(2x+3y)=25
OR repetition of eqn from S1.Not suff.

Combining we can't sove since both are basically the same equations.

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Re: A bookstore that sells used books sells each of its paperbac [#permalink]

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New post 24 Feb 2014, 04:22
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Let the price of paperbacks be 'x'
the price of hard cover book be 'y'

From Statement 1:- Joe bought 2 paperback books and 3 hardcover books for $12.50.
Thus 2x+3y = 12.50
This is one equation with 2 unknowns hence it cannot be solved. So statement 1 alone is insufficient

From Statement 2:- Paul bought 4 paperback books and 6 hardcover books for $25.00
Thus 4x+6y = 25
Again it is one equation with 2 unknowns. So statement 2 alone is insufficient.

Combining both the statements we get 2 equations:-
1. 2x+3y = 12.5
2. 4x+6y = 25

Now linear equations with 2 unknowns can only be solved it both the equations are different i.e not the same or multiplies of each other.
Here equation 2 is a multiple of equation 1. Equation 2 = (Equation 1)x2

Thus this pair of equations cannot be solved. and hence even after combining both the equations the solution is not possible.

Hence Option (E) is the answer

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Re: A bookstore that sells used books sells each of its paperbac [#permalink]

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New post 03 Jun 2014, 22:06
Bunuel wrote:
SOLUTION

A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?

We should find the value of p+h, where p is the price of one paperback and h is the price of one hard cover book.

(1) Joe bought 2 paperback books and 3 hardcover books for $12.50 --> 2p + 3h = 12.5. Not sufficient.

(2) Paul bought 4 paperback books and 6 hardcover books for $25.00 --> 4p + 6h = 25. Not sufficient.

(1)+(2) We can get 4p + 6h = 25 by multiplying 2p + 3h = 12.5 by 2, thus even when combining the statements we still have only one equation. Not sufficient.

Answer: E.




Hi Bunuel ,

Can't we get Answer as' D' by using trial and error method.

2 PB + 3 HC = 12.50$
The equation satisfies for PB =4 AND HC = 1.5 ;This is the only pair that satisifies the above equation ;
Therefore, can't we say that for one PB +one HC = 2+ 1.5 = 3.5 $

Please explain whether my approach is correct (or ) wrong.

Help is appreciated. :)

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Re: A bookstore that sells used books sells each of its paperbac [#permalink]

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New post 04 Jun 2014, 03:38
dheeraj24 wrote:
Bunuel wrote:
SOLUTION

A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?

We should find the value of p+h, where p is the price of one paperback and h is the price of one hard cover book.

(1) Joe bought 2 paperback books and 3 hardcover books for $12.50 --> 2p + 3h = 12.5. Not sufficient.

(2) Paul bought 4 paperback books and 6 hardcover books for $25.00 --> 4p + 6h = 25. Not sufficient.

(1)+(2) We can get 4p + 6h = 25 by multiplying 2p + 3h = 12.5 by 2, thus even when combining the statements we still have only one equation. Not sufficient.

Answer: E.




Hi Bunuel ,

Can't we get Answer as' D' by using trial and error method.

2 PB + 3 HC = 12.50$
The equation satisfies for PB =4 AND HC = 1.5 ;This is the only pair that satisifies the above equation ;
Therefore, can't we say that for one PB +one HC = 2+ 1.5 = 3.5 $

Please explain whether my approach is correct (or ) wrong.

Help is appreciated. :)


How did you get that p=4 and h=1.5 is the only solution of 2p + 3h = 12.5 ? What about p=4.75 and h=1, p=3.25 and h=2, ... ?
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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A bookstore that sells used books sells each of its paperbac [#permalink]

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New post 28 Mar 2016, 18:17
Here is a visual that should help.

Observations:

1) Since the cost of all the goods is the same for everyone, it is irrelevant who bought what, so don't bother complicating the question by including this information.

2) Usually, when we have two equations with two variables, this is sufficient...unless the 2nd equation happens to be the same as the first, which is what happened here.
Attachments

Screen Shot 2016-03-28 at 6.17.35 PM.png
Screen Shot 2016-03-28 at 6.17.35 PM.png [ 110.42 KiB | Viewed 3548 times ]


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Re: A bookstore that sells used books sells each of its paperbac [#permalink]

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Re: A bookstore that sells used books sells each of its paperbac   [#permalink] 02 Apr 2017, 22:49
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