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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4 postsPage 1 of 1
- payam
- GMAT 2007
Total customers = 100
Total books purchased = 200
Statement (1) - Nobody purchased more than 3 books. Not enough information INSUFFICIENT
Statement (2) - 20 customers purchased 2 books.
Total books sold to 20 customers = 40 80 Customers left = 80, Books left = 160, Not enough information. INSUFFICIENT
Combine both -
from (1) - no one bought more than 3 books, so in rest some might have bought 3 and rest of them bought just 1 book.
In 80 customers if 40 bought 3 books, no of books sold 120.
Customers left = 40
Books left = 160 - 120 = 40.
So 40 customers bought eactly 1 book. SUFFICIENT.
GMAT 2007
Total books purchased = 200
Statement (1) - Nobody purchased more than 3 books. Not enough information INSUFFICIENT
Statement (2) - 20 customers purchased 2 books.
Total books sold to 20 customers = 40 80 Customers left = 80, Books left = 160, Not enough information. INSUFFICIENT
Combine both -
from (1) - no one bought more than 3 books, so in rest some might have bought 3 and rest of them bought just 1 book.
In 80 customers if 40 bought 3 books, no of books sold 120.
Customers left = 40
Books left = 160 - 120 = 40.
So 40 customers bought eactly 1 book. SUFFICIENT.
GMAT 2007
- payam
Please, explain
I do not understand how you assume in option C that only 40 people bought 3 books. It could be 50 or 30.
- GMAT 2007
If 50 customers bought 3 books - it means 150 books sold to them, then we are left with (100 - (20+50)) = 30 customers
and (200 - (40+150)) = 10 books
30 customers, 10 books - not possible because 20 customers will left with no books to purchase. Similarly, if
30 customers bought 3 books = it means 90 books sold to them, then we are left with (100-(20+30)) = 50 customers
and (200-(40+90)) = 70 books
50 customers, 70 books, if each of them bought 1 book - we are still left with 20 books.Not possible, because we know only 20 customers bought 2 books and no one bought more than 3.
So only possible combination is 40 customers bought 3 books and rest 40 bought exactly 1 book.
Hope it helps
GMAT 2007
and (200 - (40+150)) = 10 books
30 customers, 10 books - not possible because 20 customers will left with no books to purchase. Similarly, if
30 customers bought 3 books = it means 90 books sold to them, then we are left with (100-(20+30)) = 50 customers
and (200-(40+90)) = 70 books
50 customers, 70 books, if each of them bought 1 book - we are still left with 20 books.Not possible, because we know only 20 customers bought 2 books and no one bought more than 3.
So only possible combination is 40 customers bought 3 books and rest 40 bought exactly 1 book.
Hope it helps
GMAT 2007
4 posts Page 1 of 1