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A total of 100 customers purchased books at a certain bookstore last

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

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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 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.
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 12 Sep 2008, 09:40
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: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 12 Sep 2008, 11:29
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: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 12 Sep 2008, 12:21
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1
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: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 12 Sep 2008, 12:51
1
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: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 12 Sep 2008, 13:22
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: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 13 Sep 2008, 23:46
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: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 12 Nov 2008, 15:57
botirvoy 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+b+c=100 < from the stem+statement 1

a+2b+3c=200 < from stem+statment1 Insuff

a+2(20)+3c=200
a+20+c=100

C it is..
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 12 Nov 2008, 18:22
botirvoy 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.


B.

2: total = 1n + 2x20 + 3(100-20-n)
200 = n + 40 + 240 - 3n
2n = 80
n = 40
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post Updated on: 13 Nov 2008, 07:55
GMAT TIGER wrote:
Can you guys explain on how it is C?

GMAT TIGER, the way you solved it, you assumed statement 1 as well.

I can confirm, OA is C.
Cheers guys!

Originally posted by seofah on 13 Nov 2008, 07:35.
Last edited by seofah on 13 Nov 2008, 07:55, edited 1 time in total.
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 13 Nov 2008, 07:41
botirvoy wrote:
GMAT TIGER wrote:
Can you guys explain on how it is C?

GMAT TIGER, in the way you solved it, you assumed statement as well.

I can confirm, OA is C.
Cheers guys!


agreed but a million dollor question: why is it so easy to overlook a very simple thing? :twisted: :evil:
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 15 Jun 2013, 09:24
seofah wrote:
GMAT TIGER wrote:
Can you guys explain on how it is C?

GMAT TIGER, the way you solved it, you assumed statement 1 as well.

I can confirm, OA is C.
Cheers guys!


I got B as well and while I did assume statement 1, I got it from the question. Here's my reasoning:

Since it is given at the question stem that "100 customers purchased books" I assumed that every one of them buys at least 1 book (since purchasing 0 books doesn't make sense). Therefore, none of the 100 customers can buy more than 3 books (if 1 customer buys 4 books it means 1 will buy 0 books to average 2 books per customer - another given). To me - statement 1 is implied.

I just can't get past this "100 customers purchased books" part. If they rephrased to "100 customers visited a bookstore and purchased a total of 200 books" then my answer will be C.
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 15 Jun 2013, 09:50
ctw21 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.

I got B as well and while I did assume statement 1, I got it from the question. Here's my reasoning:

Since it is given at the question stem that "100 customers purchased books" I assumed that every one of them buys at least 1 book (since purchasing 0 books doesn't make sense). Therefore, none of the 100 customers can buy more than 3 books (if 1 customer buys 4 books it means 1 will buy 0 books to average 2 books per customer - another given). To me - statement 1 is implied.

I just can't get past this "100 customers purchased books" part. If they rephrased to "100 customers visited a bookstore and purchased a total of 200 books" then my answer will be C.


For (2) we have that 20 customers purchased total of 40 books. Thus the remaining 80 customers purchased 160 books.

Now, consider the following scenarios:
79 customers purchased 1 book each and 1 customer purchased 81 books;
78 customers purchased 1 book each and 2 customer purchased 41 books.

So, this statement is not sufficient.

Answer C is correct.
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 15 Jun 2013, 10:06
Bunuel wrote:
ctw21 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.

I got B as well and while I did assume statement 1, I got it from the question. Here's my reasoning:

Since it is given at the question stem that "100 customers purchased books" I assumed that every one of them buys at least 1 book (since purchasing 0 books doesn't make sense). Therefore, none of the 100 customers can buy more than 3 books (if 1 customer buys 4 books it means 1 will buy 0 books to average 2 books per customer - another given). To me - statement 1 is implied.

I just can't get past this "100 customers purchased books" part. If they rephrased to "100 customers visited a bookstore and purchased a total of 200 books" then my answer will be C.


For (2) we have that 20 customers purchased total of 40 books. Thus the remaining 80 customers purchased 160 books.

Now, consider the following scenarios:
79 customers purchased 1 book each and 1 customer purchased 81 books;
78 customers purchased 1 book each and 2 customer purchased 41 books.

So, this statement is not sufficient.

Answer C is correct.


Now I see. Many thanks!
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 20 Jul 2013, 05:54
If we take both statement

St 2: 20( customer) X 2 = 40 books

Now we have 80 customer with 160 books

50 customer X 3 books = 150 books ---- stat 1

10 customer X 1 book = 10 books

remaining 20 did not buy any book ---- is this possible?
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 20 Jul 2013, 06:05
Mountain14 wrote:
If we take both statement

St 2: 20( customer) X 2 = 40 books

Now we have 80 customer with 160 books

50 customer X 3 books = 150 books ---- stat 1

10 customer X 1 book = 10 books

remaining 20 did not buy any book ---- is this possible?


From a+c=80 and a+3c=160 it follows that a=40 and c=40.

40 customers purchased 1 book each --> total = 40;
20 customers purchased 2 books each --> total = 40;
40 customers purchased 3 books each --> total = 120;

Total = 200.

Hope it helps.
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 20 Jul 2013, 06:13
Bunuel wrote:
Mountain14 wrote:
If we take both statement

St 2: 20( customer) X 2 = 40 books

Now we have 80 customer with 160 books

50 customer X 3 books = 150 books ---- stat 1

10 customer X 1 book = 10 books

remaining 20 did not buy any book ---- is this possible?


From a+c=80 and a+3c=160 it follows that a=40 and c=40.

40 customers purchased 1 book each --> total = 40;
20 customers purchased 2 books each --> total = 40;
40 customers purchased 3 books each --> total = 120;

Total = 200.

Hope it helps.



Thanks for your quick reply....

But my main question is- can there be a scenario that some customer did not buy any book? How do we know from such DS question..

In case of other DS question, Zero play important part .... :(
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 20 Jul 2013, 06:21
Mountain14 wrote:
Bunuel wrote:
Mountain14 wrote:
If we take both statement

St 2: 20( customer) X 2 = 40 books

Now we have 80 customer with 160 books

50 customer X 3 books = 150 books ---- stat 1

10 customer X 1 book = 10 books

remaining 20 did not buy any book ---- is this possible?


From a+c=80 and a+3c=160 it follows that a=40 and c=40.

40 customers purchased 1 book each --> total = 40;
20 customers purchased 2 books each --> total = 40;
40 customers purchased 3 books each --> total = 120;

Total = 200.

Hope it helps.



Thanks for your quick reply....

But my main question is- can there be a scenario that some customer did not buy any book? How do we know from such DS question..

In case of other DS question, Zero play important part .... :(


We are told that a total of 100 customers purchased books, so each purchased at least 1 book.
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 03 Dec 2013, 06:33
seofah 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.


For statement 2, we are told that 20 of the customers purchased only 2 books each.
That of course isn't sufficient/

Now we have 160 books remaining and 80 customers too.
We can have that none purchased one book each of the 80 remaining purchased 2 books each, I believe that that's the only way. Given the restriction of no more than 3 books

Hence C

Is this correct?
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Re: A total of 100 customers purchased books at a certain bookstore last  [#permalink]

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New post 28 Oct 2016, 02:46
x2suresh 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



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.


-------------------------------------------------------------
Hi suresh,

How'd you get?

x+y=80
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Re: A total of 100 customers purchased books at a certain bookstore last &nbs [#permalink] 28 Oct 2016, 02:46

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