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Re: A certain novel is available in hardcover and paperback. lf the store [#permalink]
1
Kudos
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.
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Re: A certain novel is available in hardcover and paperback. lf the store [#permalink]
1
Kudos
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.

Answer (A)
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Re: A certain novel is available in hardcover and paperback. lf the store [#permalink]
1
Kudos
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.
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Re: A certain novel is available in hardcover and paperback. lf the store [#permalink]
1
Kudos
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.

Answer A.
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Re: A certain novel is available in hardcover and paperback. lf the store [#permalink]
1
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Expert Reply
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
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Re: A certain novel is available in hardcover and paperback. lf the store [#permalink]
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
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Re: A certain novel is available in hardcover and paperback. lf the store [#permalink]
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