Data Sufficiency

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.


OA C

It is C)


Stmt 1)

Let x be the customer who purchased 1 book
y - 2 books
z- 3 books

To find x

x+y+z=100


x(1)+y(2)+z(3) / 100 = 2

x+2y+3z = 200

INSUFF 2 eqns 3 vars

Stmt 2: y=20

x+y+z = 100
x+20+z=100
x+z=80

1 eqn 2 variables

INSUFF

Combine 1) and 2)

x+2y+3z = 200
x+2(20)+3z = 200
x+3z=160

AND
x+z=80

x=40 y=20 z=40

40*1+20*2 +40*3 = 200 books 100 customers

vishubn 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.


OA C

Lets start with the easy statement. (1) does not give any information about customers who purchased 1 book ? A and D are GONE!

(2) only tells us 20x2=40 books are purchased and we still need to find out what happened to the 160 books and 80 customers ?

B is gone!

so if we can solve this problem it is C otherwise we will pick E

well (1) says None of the customers purchased more than 3 books..AHA!! so it means people either purchased 1, 2 or 3 books. We know how many purchased 2 books so:

Remaning 80 customers either purchased 1 or 3 books and we have to find how many purchased 1 book ? Lets call it X

X (1 book) + ( 80-X) (3 books ) = 160

you dont need to solve it after this point.

You have one equation and one variable!

Choose C! dont waste your time. 8)