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

Question

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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x2suresh · Accepted Answer

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.

brokerbevo · Answer

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

seofah · Answer

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

I can confirm, OA is C.
Cheers guys!

ctw21 · Answer

I got B 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.

Bunuel · Answer

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.

HarveyS · Answer

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?

Bunuel · Answer

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.

HarveyS · Answer

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 ....

Bunuel · Answer

We are told that a total of 100 customers  purchased  books, so each purchased at least 1 book.

Rohanx9 · Answer

Need to find n1

from 1)
n_1+n_2+n_3=100
2n_1+2n_2+3n_3=200

three variables, two equations = not solvable.

from 1 and 2)
n_1 + 20 + n_3 = 100
2n_1 + 40 + 3n_3 = 200

two variables, two equations = solvable.

Both statements are required. Answer C

KarishmaB · Answer

Total 100 customers and 200 books so each customer purchased on average 2 books. (1) None of the customers purchased more than 3 books. Then only 1, 2 or 3 books were purchased with an average of 2. Think in terms of deficit = excess. If 10 customers purchased only 1 book, then 10 purchased 3 books. We don't know how many purchased only 1 book. Not sufficient alone. (2) 20 of the customers purchased only 2 books each. If 20 customers purchased 2 books, then 80 customers purchased 1 or 3 or more books. We don't know how many purchased on 1 book. Not sufficient alone. Using both, we get that 20 customers purchased 2 books and 80 purchased 1 or 3. To get the avg of 2, 40 must have purchased 1 book and 40 must've purchased 3. Answer (C) Pm: How is this question different from https://gmatclub.com/forum/in-a-photo-c ... l#p3632803 In the books question, we are talking about people who bought books so each of the 200 bought at least 1 book. In the photos questions, it is possible that Julia got no prize in one or two of the categories.

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

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