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A total of 100 customers purchased books at a certain

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Manager
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Joined: 10 Oct 2008
Posts: 56

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A total of 100 customers purchased books at a certain [#permalink]

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New post 08 Nov 2008, 18:21
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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 the 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:

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Re: customers and books ---29 [#permalink]

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New post 08 Nov 2008, 18:34
Jcpenny 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 the 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:


the answer is (C)


let us assume that C1 = consumners who purchased 1 Book
similarly C2= consumners who purchased 2 Books
C3 , C3 , ........


from the equation

1*C1 + 2*C2 + 3*C3 + ........= 200 ---------(1)

C1 + C2 + C3 + C4 + ...........=100 ----------(2)

Now let us test (I)
if no consumer purchased more than 3 books then our equations (1) and (2) will be

1*C1 + 2*C2 + 3*C3 = 200 ---------(1)
C1 + C2 + C3 = 100 ----------(2)

3 unknowens with 2 equation
---Insufficient

test (II)
we will get another equation which is
C2 = 20

however we have unlimited variables C1, C2, C3, C4 .......



test (I) and (II) together

we will have 3 equation and 3 unknowens
1*C1 + 2*C2 + 3*C3 = 200 ---------(1)
C1 + C2 + C3 = 100 ----------(2)
C2 = 20-----------------(3)


which is sufficient

so solution is (c)

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Re: customers and books ---29 [#permalink]

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New post 08 Nov 2008, 18:41
Agree did the same

x+y+z = 100

(1) says 3x+ 2y + z =200

2 eq's 3 unknowns ,Insuff

(2) says 2y=40

x+z 80 Insuff

Together, 3 unknowns, 3 eqs can find x.

Kudos [?]: 423 [0], given: 1

Re: customers and books ---29   [#permalink] 08 Nov 2008, 18:41
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