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Math Expert V
Joined: 02 Sep 2009
Posts: 59622
A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 64% (02:00) correct 36% (01:26) wrong based on 28 sessions

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Competition Mode Question

A certain novel is available in hardcover and paperback. If the store stocks a total of 100 copies of this book, how many are paperbacks?

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.

_________________
Director  P
Joined: 18 May 2019
Posts: 534
Re: A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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1
We know from the question stem that H + P = 100 .................(1)
where H is the number of hardcover novels, and P is the number of paperback novels.
We are to determine the number of paperback novels available out of the total stock of 100 novels.

Statement 1:
If twenty hardcover versions are sold, there would be three times as many hardcover versions left as paperback versions.
Statement 1 is sufficient. This is because we are able to determine that out of the 80 novels left in stock after selling 20 hardcover versions, the ration of H:P=3:1; hence we can calculate the number of paperback versions left in stock to be 20. In addition, since the 20 previously sold were hardcover, then it means the total paperback that was in stock is also 20.

Statement 2: says that if a hardcover version costs twice as much as a paperback version, the total sales of all the books in stock will be \$90.
Statement 2 is not sufficient.
Assuming that a paperback version costs \$0.5, then a hardcover costs \$1.
from (1) we can say H=100-P
100-P + 0.5P = 90
P=20.

however if a paperback costs \$0.6 then a hardcover costs \$1.2
1.2(100-P)+0.6P = 90
120P -1.2P +0.6P =90
0.6P=30
P=50.

We can conclude that Statement 1 alone is sufficient. The answer has to be therefore A in my view.
Manager  S
Joined: 05 Aug 2018
Posts: 72
Location: Thailand
Concentration: Finance, Entrepreneurship
GPA: 3.68
WE: Business Development (Energy and Utilities)
Re: A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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1
A certain novel is available in hardcover and paperback. If the store stocks a total of 100 copies of this book, how many are paperbacks?

Let's number of Hardcover books = H and number of paperback books = P
H + P = 100, Find P?

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.

H - 20 = 3P
H - 3P = 20
Solve P, with the equation that given; 4P = 80 -> P = 20

Therefore, (1) alone is sufficient

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.

let's x = cost of one paperback book
2xH + Px = 90 - 2 equations, 3 variables - cant solve P.

Therefore (2) is not sufficient.

Thus, A is the correct answer choice.
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5466
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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1
hc+pb=100
find PB
#1
If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.
H-20=3*Pb
H=3*Pb+20
3*Pb+20+Pb=100
4Pb=80
Pb=20
sufficient
#2
If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.

Cost of Hc =2*Pb
x*Hc+y*Pb=90
given x+y=100
2*Pb*x+y*Pb=100
we have 2 unknows ; insufficient
IMO A sufficient

A certain novel is available in hardcover and paperback. If the store stocks a total of 100 copies of this book, how many are paperbacks?

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.
Director  P
Joined: 24 Nov 2016
Posts: 935
Location: United States
Re: A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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1
Quote:
A certain novel is available in hardcover and paperback. If the store stocks a total of 100 copies of this book, how many are paperbacks?

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining: sufic.

h-20=3p…h=3p+20; h+p=100…3p+20+p=100…p=20

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90: insufic.

Senior Manager  P
Joined: 10 Apr 2018
Posts: 281
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34 GPA: 3.3
Re: A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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1
Quote:
A certain novel is available in hardcover and paperback. If the store stocks a total of 100 copies of this book, how many are paperbacks?

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.

Let there be p paperback and h hardcover books.
So, p+h=100
We have to find value of p.

(1) (h-20)=3p
=> h=3p+20
From the above equation and h+p=100, value of p can be found.
Thus, sufficient.

(2) Let the cost of paperback be c.
So, h(2c)+p(c)=90
Above equation combined with p+h=100 doesn't give a unique value of p.
Thus, insufficient.

Therefore, the correct answer is option A.
Senior Manager  P
Joined: 07 Mar 2019
Posts: 442
Location: India
GMAT 1: 580 Q43 V27 WE: Sales (Energy and Utilities)
Re: A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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1
A certain novel is available in hardcover and paperback. If the store stocks a total of 100 copies of this book, how many are paperbacks?

Let number of paperback copes of novel = x
Then number of hardcover copes of novel = 100 - x

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.

Remaining number of hardcover copes of novel = 100 - x - 20 = 80 - x
Assuming that only hardcover were sold than remaining number of paperback = x
Now 3x = 80 - x
x = 20

SUFFICIENT.

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.

Let cost o hardcover = Ch
Cost o paperback = Cp
and Ch = 2Cp

Now, x * Cp + (100 - x) * Ch = 90
x * Cp + (100 - x) * 2Cp = 90

INSUFFICIENT.

_________________
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Manager  G
Joined: 17 Jan 2019
Posts: 127
Re: A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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A certain novel is available in hardcover and paperback. If the store stocks a total of 100 copies of this book, how many are paperbacks?

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.

we don't know how many paperback versions were sold.
Therefore, insufficient

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.

H+P=100
H+2P=90

two variables two equations.
sufficient

therefore, B
Math Expert V
Joined: 02 Aug 2009
Posts: 8289
Re: A certain novel is available in hardcover and paperback. lf the store  [#permalink]

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1
A certain novel is available in hardcover and paperback. If the store stocks a total of 100 copies of this book, how many are paperbacks?

Purely by equation and variables...
p+h=100, so one equation and 2 variables... ONE more equation required.

(1) If 20 hardcover versions of this book were sold, there would be three times as many hardcover versions of the book remaining as paperback versions of the book remaining.
Another equation, so sufficient...
After 20 h are sold, h-20 remain, so h-20=3p.....100-p-20=3p......4p=80....p=20

(2) If the hardcover version of the book cost twice as much as the paperback version of the book, the total sales of all books in stock would yield \$90.
Another equation, but another variable cost added, so insufficient..
Let the cost of paperback be x, so hardcover would cost 2x..2x(h)+x(p)=90...2xh+x(100-h)=90....100x+xh=90

A
_________________ Re: A certain novel is available in hardcover and paperback. lf the store   [#permalink] 15 Oct 2019, 19:08
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