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A total of 100 customers purchased books at a certain

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A total of 100 customers purchased books at a certain [#permalink]  12 Sep 2008, 10:14
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A total of 100 customers purchased books at a certain bookstore last week. If these customers purchased a total of 200 books, how many of these customers purchased only 1 book each?

1) None of the customers purchased more than 3 books

2) 20 of the customers purchased only 2 books each
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Re: DS - Books [#permalink]  12 Sep 2008, 10:40
E

A and B are insufficient by themselves. C is insufficient because B simply indicates that 160 is the number of remaining books (where some combination of 3 books and 1 book are bought). More than one combination exists.
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Re: DS - Books [#permalink]  12 Sep 2008, 12:29
A ?

(1) None purchased > 3, so they must have purchased 2,1 or 0 books?

200 books in total purchased by 100 people. Going by (1) all would have purchased atleast 2 books.
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Re: DS - Books [#permalink]  12 Sep 2008, 13:21
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IgnitedMind wrote:
A total of 100 customers purchased books at a certain bookstore last week. If these customers purchased a total of 200 books, how many of these customers purchased only 1 book each?

1) None of the customers purchased more than 3 books

2) 20 of the customers purchased only 2 books each

C.
20 --> 2 books == 40 books

160 books left and these books need to be distributed between x and y
x= no of customers purchased only 1 book
y= no of customer purchased 3 books.

x+3y=160
x+y=80

y=x=40.
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Re: DS - Books [#permalink]  12 Sep 2008, 13:51
IgnitedMind wrote:
A total of 100 customers purchased books at a certain bookstore last week. If these customers purchased a total of 200 books, how many of these customers purchased only 1 book each?

1) None of the customers purchased more than 3 books

2) 20 of the customers purchased only 2 books each

C.

(1) The customers either purchased 1 book, 2 books, or 3 books
a = people who purchased 1 book
b = people who purchased 2 books
c = people who purchased 3 books

3c + 2b + a = 200 books
a + b + c = 100 people ---> From here, we have 3 variables and only 2 equations --> INSUFF

(2) states that b = 20 INSUFF

Together:
First equation: 3c + 2(20) + a = 200 ---> 3c + a = 160 --> a = 160 - 3c
Second equation: a + 20 + c = 100 --> a + c = 80
Substitution (both equations): 160 - 3c + c = 80 --> c = 40, so a = 40 and b = 20 ---> SUFFICIENT
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Re: DS - Books [#permalink]  12 Sep 2008, 14:22
I get C as well..

people=100

books=200

we are told that
1) no one buys more than 3 books..

ok..so maybe 90 people bought 2 book each, 3 people would bought 3 books each and 1 person bought 1 book.. i can play with numbers around..easy to see Insuff

2) says 20 people bought 2 books each..well the maybe 1 person bought 160 remaining books ..again insuff

together

x=people bought 1 book, y=people bought 3 books

x+y=80

books =160

3x+y=160
x+y=80 solve for x=40
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Re: DS - Books [#permalink]  12 Sep 2008, 14:31
(1) Ah!! I took it more than 3, missed that it can even be 3...darn
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Re: DS - Books [#permalink]  14 Sep 2008, 00:46
IgnitedMind wrote:
A total of 100 customers purchased books at a certain bookstore last week. If these customers purchased a total of 200 books, how many of these customers purchased only 1 book each?

1) None of the customers purchased more than 3 books

2) 20 of the customers purchased only 2 books each

(1) INSUFFI ,say x people bought 1 book,y got 2 books and z got 3
then x+2y+3z=200 and x+y+z=100 cant solve

2) x+z=80 and x+3y=200 => x=20 and z=60 SOLVES SUFFI
IMO B
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Re: DS - Books [#permalink]  14 Sep 2008, 00:48
spriya wrote:
IgnitedMind wrote:
A total of 100 customers purchased books at a certain bookstore last week. If these customers purchased a total of 200 books, how many of these customers purchased only 1 book each?

1) None of the customers purchased more than 3 books

2) 20 of the customers purchased only 2 books each

(1) INSUFFI ,say x people bought 1 book,y got 2 books and z got 3
then x+2y+3z=200 and x+y+z=100 cant solve

2) x+z=80 and x+3y=200 => x=20 and z=60 SOLVES SUFFI
IMO B

OMG !!i used info of (1) in (2) ...i agree with OA C
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Re: DS - Books   [#permalink] 14 Sep 2008, 00:48
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