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# A bookman purchased 30 copies of a new book released recently, 10 of

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Manager
Joined: 10 Feb 2011
Posts: 104
A bookman purchased 30 copies of a new book released recently, 10 of  [#permalink]

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17 Feb 2011, 15:11
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Difficulty:

55% (hard)

Question Stats:

66% (02:52) correct 34% (02:33) wrong based on 76 sessions

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A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Math Expert
Joined: 02 Sep 2009
Posts: 58385
Re: A bookman purchased 30 copies of a new book released recently, 10 of  [#permalink]

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17 Feb 2011, 16:21
3
banksy wrote:
193. A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

12 copies were sold, hence 30-12=18 copies were left. Let # of paperback copies left be p then 15p+20(18-p)=280 --> p=16 --> # of paperback copies sold is 20-16=4.

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Re: A bookman purchased 30 copies of a new book released recently, 10 of  [#permalink]

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21 Oct 2018, 04:14
banksy wrote:
A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

Since 10 of the 30 books are hardback, the remaining 20 books are paperback.
Since 12 of the 30 books are sold, the total number of unsold books = 30-12 = 18.
We can PLUG IN THE ANSWERS, which represent the number of paperback books that are sold.
When the correct answer is plugged in, the total value of the unsold books = 280.

B: 6
Since 6 of the 20 paperback books are sold, the number of unsold paperback books = 20-6 = 14.
Since the total number of unsold books = 18, the number of unsold hardback books = 18-14 = 4.
Since the 14 unsold paperback books are priced at $20 each, while the 4 unsold hardback books are priced at$15 each, the total value of unsold books = (14*20) + (4*15) = 280 + 60 = 340.
The total value of the unsold books is TOO HIGH.
To reduce the total value of the unsold books, the less expensive type of book -- paperback -- must constitute a greater proportion of the unsold books.
Implication:
Fewer paperback books must be sold, so that a greater number of paperback books remain UNSOLD.

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Re: A bookman purchased 30 copies of a new book released recently, 10 of  [#permalink]

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21 Oct 2018, 05:35
GMATGuruNY wrote:
banksy wrote:
A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

Since 10 of the 30 books are hardback, the remaining 20 books are paperback.
Since 12 of the 30 books are sold, the total number of unsold books = 30-12 = 18.
We can PLUG IN THE ANSWERS, which represent the number of paperback books that are sold.
When the correct answer is plugged in, the total value of the unsold books = 280.

B: 6
Since 6 of the 20 paperback books are sold, the number of unsold paperback books = 20-6 = 14.
Since the total number of unsold books = 18, the number of unsold hardback books = 18-14 = 4.
Since the 14 unsold paperback books are priced at $20 each, while the 4 unsold hardback books are priced at$15 each, the total value of unsold books = (14*20) + (4*15) = 280 + 60 = 340.
The total value of the unsold books is TOO HIGH.
To reduce the total value of the unsold books, the less expensive type of book -- paperback -- must constitute a greater proportion of the unsold books.
Implication:
Fewer paperback books must be sold, so that a greater number of paperback books remain UNSOLD.

Nice Approach.However I had a query.

When I read the question stem for the first time.

A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

I was confused if already 10 are hard back and sold $20 and remaining are paperpack and sold for$15..Why does it again reiterate If 12 copies were sold...

Math Expert
Joined: 02 Aug 2009
Posts: 7961
A bookman purchased 30 copies of a new book released recently, 10 of  [#permalink]

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21 Oct 2018, 06:40
1
1
banksy wrote:
A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

Now let us look at different ways to do this question

(I) Weighted average
If you know this, I would surely recommend this
total books unsold = $$30-12=18$$
cost of these 18 books is 280..
Had all these been H 20 per book, cost would be 18*20=360
And Had all these been P @ 15 per book, cost would be 18*15=270
so Number of books of P = $$18*\frac{360-280}{360-270}=18*\frac{8}{9}=16$$
so 16 out of 20 paperback are unsold and remaining 4 are sold

(II) Substitution
If you are stuck, I would recommend this
let us take choice A - 4..
so 4 out of 20 paperback are sold, and remaining 16 are unsold, costing $$16*15=240$$
Total unsold is 18, so 18-16 or 2 are hardback, costing 2*20=40
total cost of unsold, thus, is $$240+40=280$$ and given is also 280
so choice A is correct

(III) Algebraic
there can be two equations...
$$H+P=12.......H=12-P$$...(i)
$$20*(10-H)+15*(20-P)=280..........200-20H+300-15P=280..........20H+15P=220$$
substitute value of H in it
$$20(12-P)+15P=220.........240-20P+15P=220.........5P=20....P=4$$

A
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Re: A bookman purchased 30 copies of a new book released recently, 10 of  [#permalink]

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21 Oct 2018, 07:23
chetan2u wrote:
banksy wrote:
A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

Now let us look at different ways to do this question

(I) Weighted average
If you know this, I would surely recommend this
total books unsold = $$30-12=18$$
cost of these 18 books is 280..
Had all these been H 20 per book, cost would be 18*20=360
And Had all these been P 20 per book, cost would be 18*15=270
so Number of books of P = $$18*\frac{360-280}{360-270}=18*\frac{8}{9}=16$$
so 16 out of 20 paperback are unsold and remaining 4 are sold

(II) Substitution
If you are stuck, I would recommend this
let us take choice A - 4..
so 4 out of 20 paperback are sold, and remaining 16 are unsold, costing $$16*15=240$$
Total unsold is 18, so 18-16 or 2 are hardback, costing 2*20=40
total cost of unsold, thus, is $$240+40=280$$ and given is also 280
so choice A is correct

(III) Algebraic
there can be two equations...
$$H+P=12.......H=12-P$$...(i)
$$20*(10-H)+15*(20-P)=280..........200-20H+300-15P=280..........20H+15P=220$$
substitute value of H in it
$$20(12-P)+15P=220.........240-20P+15P=220.........5P=20....P=4$$

A

When I read the question stem for the first time.

A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

I was confused if already 10 are hard back and sold $20 and remaining are paperpack and sold for$15..Why does it again reiterate If 12 copies were sold...

Math Expert
Joined: 02 Aug 2009
Posts: 7961
Re: A bookman purchased 30 copies of a new book released recently, 10 of  [#permalink]

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21 Oct 2018, 07:29
1
prabsahi wrote:
chetan2u wrote:
banksy wrote:
A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

Now let us look at different ways to do this question

(I) Weighted average
If you know this, I would surely recommend this
total books unsold = $$30-12=18$$
cost of these 18 books is 280..
Had all these been H 20 per book, cost would be 18*20=360
And Had all these been P 20 per book, cost would be 18*15=270
so Number of books of P = $$18*\frac{360-280}{360-270}=18*\frac{8}{9}=16$$
so 16 out of 20 paperback are unsold and remaining 4 are sold

(II) Substitution
If you are stuck, I would recommend this
let us take choice A - 4..
so 4 out of 20 paperback are sold, and remaining 16 are unsold, costing $$16*15=240$$
Total unsold is 18, so 18-16 or 2 are hardback, costing 2*20=40
total cost of unsold, thus, is $$240+40=280$$ and given is also 280
so choice A is correct

(III) Algebraic
there can be two equations...
$$H+P=12.......H=12-P$$...(i)
$$20*(10-H)+15*(20-P)=280..........200-20H+300-15P=280..........20H+15P=220$$
substitute value of H in it
$$20(12-P)+15P=220.........240-20P+15P=220.........5P=20....P=4$$

A

When I read the question stem for the first time.

A bookman purchased 30 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for$15 each. If 12 copies were sold and the total value of the remaining books was 280, how many paperback copies were sold?

I was confused if already 10 are hard back and sold $20 and remaining are paperpack and sold for$15..Why does it again reiterate If 12 copies were sold...

Hi..
The give away is the verb ARE..
These are sold for 50$would mean these are priced at 50$..
Had it been these were sold for 50$, yes it would mean they have already been sold... . _________________ Senior Manager Joined: 09 Jun 2014 Posts: 352 Location: India Concentration: General Management, Operations Re: A bookman purchased 30 copies of a new book released recently, 10 of [#permalink] ### Show Tags 21 Oct 2018, 07:33 Hi.. The give away is the verb ARE.. These are sold for 50$ would mean these are priced at 50$.. Had it been these were sold for 50$, yes it would mean they have already been sold...

.[/quote]

So its more like Jeans are sold for $20.(MEANS its priced at$20)

Thank you so much.Just wanted to make sure I don't have the same GAP for new problems of this type.
Re: A bookman purchased 30 copies of a new book released recently, 10 of   [#permalink] 21 Oct 2018, 07:33
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