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# A bookstore that sells used books sells each of its paperbac

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A bookstore that sells used books sells each of its paperbac [#permalink]  23 Feb 2014, 06:48
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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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Math Expert
Joined: 02 Sep 2009
Posts: 28734
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Kudos [?]: 47211 [0], given: 7113

Re: A bookstore that sells used books sells each of its paperbac [#permalink]  23 Feb 2014, 06:48
Expert's post
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.

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Re: A bookstore that sells used books sells each of its paperbac [#permalink]  23 Feb 2014, 23:27
1
KUDOS
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]  24 Feb 2014, 02:48
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]  24 Feb 2014, 03:22
1
KUDOS
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]  01 Mar 2014, 04:30
Expert's post
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.

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Re: A bookstore that sells used books sells each of its paperbac [#permalink]  03 Jun 2014, 21:06
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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 28734
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Kudos [?]: 47211 [0], given: 7113

Re: A bookstore that sells used books sells each of its paperbac [#permalink]  04 Jun 2014, 02:38
Expert's post
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.

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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Re: A bookstore that sells used books sells each of its paperbac   [#permalink] 04 Jun 2014, 02:38
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# A bookstore that sells used books sells each of its paperbac

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