Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Thabo owns exactly 140 books, and each book is either paperback fictio [#permalink]

Show Tags

14 Jun 2016, 13:22

2

This post received KUDOS

11

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

81% (01:52) correct 19% (02:13) wrong based on 792 sessions

HideShow timer Statistics

Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?

Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?

Let x = the number of paperback fiction books y = the number of paperback nonfiction books z = the number of hardcover nonfiction books

From the first sentence we have Equation #1: x + y + z = 140

"...he owns 20 more paperback nonfiction books than hardcover nonfiction books ..." Equation #2: y = 20 + z

"...twice as many paperback fiction books as paperback nonfiction books..." Equation #3: x = 2y

Solve equation #2 for z: z = y - 20 Now, we can replace both x and z with y in Equation #1

2y + y + (y - 20) = 140

4y - 20 = 140

4y = 160

y = 40

There are 40 paperback nonfiction books. This is 20 more than the number of hardcover nonfiction books, so z = 20. That's the answer. Just as a check, x = 80, and 80 + 40 + 20 = 140.

Answer = 20, (B)

Does all this make sense? Mike
_________________

Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

My friend, I've looked over your post several times and I cannot for the life of me tell what you are doing. A big part of mathematical thinking is organization, and especially in this public forum, your goal should be to present everything, including your questions, as clearly as possible. Begin by labeling all your variables clearly in words. Then make clear which equations you are taking from the prompt information. Then, make clear how you are combining them. In your post, I see both a lower case y and a capital Y: it's not clear to me whether this is a typo or whether you intend these to be two different variables. Having the same letter, uppercase and lowercase, as two different variable would be a less than optimal choices. This problem really requires three variables, and I don't see that clearly in your work. If you make your question as clear as possible, then you are much more likely to get a helpful response from one of the experts here.

Re: Thabo owns exactly 140 books, and each book is either paperback fictio [#permalink]

Show Tags

10 Aug 2016, 20:37

I think we can use double-matrix method and solve using only one variable.

Our goal is to find the number of hardcover nonfiction books. Let that number be x. We are given that all 140 books are either paperback fiction, paperback nonfiction, or hardcover nonfiction. This implies that number of hardcover fiction books is 0.

Double-matrix: P = paperback; H = hardcover; F = fiction; NF = nonfiction

Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?

A) 10 B) 20 C) 30 D) 40 E) 50

We are given that Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction.

We can let f = the number of paperback fiction books, n = the number of paperback nonfiction books, and h = the number of hardcover nonfiction books.

Since Thabo has 140 books, we can say:

f + n + h = 140

We are also given that Thabo owns 20 more paperback nonfiction books than hardcover nonfiction books and twice as many paperback fiction books as paperback nonfiction books. Thus, we can say:

n = 20 + h

AND

f = 2n

We need to determine how many hardcover nonfiction books Thabo owns.

Since we have the variable n in each equation, we should get each variable in terms of n.

h = n - 20 and f = 2n

Finally, we can substitute n - 20 for h and 2n for f in the equation f + n + h = 140, so we have:

Re: Thabo owns exactly 140 books, and each book is either paperback fictio [#permalink]

Show Tags

02 Dec 2016, 08:01

mikemcgarry wrote:

AbdurRakib wrote:

Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?

Let x = the number of paperback fiction books y = the number of paperback nonfiction books z = the number of hardcover nonfiction books

From the first sentence we have Equation #1: x + y + z = 140

"...he owns 20 more paperback nonfiction books than hardcover nonfiction books ..." Equation #2: y = 20 + z

"...twice as many paperback fiction books as paperback nonfiction books..." Equation #3: x = 2y

Solve equation #2 for z: z = y - 20 Now, we can replace both x and z with y in Equation #1

2y + y + (y - 20) = 140

4y - 20 = 140

4y = 160

y = 40

There are 40 paperback nonfiction books. This is 20 more than the number of hardcover nonfiction books, so z = 20. That's the answer. Just as a check, x = 80, and 80 + 40 + 20 = 140.

Answer = 20, (B)

Does all this make sense Mike

twice as many paperback fiction books as paperback nonfiction books

Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?

My friend, this is 100% correct as it is. You see, the situation is static and there is no comparison conducted. Consider the question: 1) How many books do you own? That question is perfectly correct. In that question, I am asking how many books are in your possession right now. The question does not consider any comparison at all, whether to your own past or future or with some other book owner. By contrast, this question sounds awkward: 2) How many more books do you own? To a native-speaker's ears, that sounds incomplete. The obvious question left hanging is "more than what??" If you had been discussing how many books you bought in the past month, then in that context, #2 might be a sensible question because there's already an implicit comparison. We do that sort of thing in real language--build logical links from one sentence to the next.

That happens in real language, but in the artificiality of the GMAT, each problem is a self-contained entity. This problem makes comparisons among the various kinds of books, but the prompt question itself is not a comparison. The prompt question itself is a question about the static fixed number in existence: "how many books?" Including the word "more" would be wrong.

Does all this make sense? Mike
_________________

Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

This question can be solved by TESTing THE ANSWERS. We're given several facts to work with:

1) Total number of books = 140 and there are only 3 types of books. 2) Paperback Nonfiction = 20 + Hardcover Nonfiction 3) Paperback Fiction = 2(Paperback Nonfiction)

We're asked for the number of Hardcover Nonfiction books.

Given the 2nd and 3rd facts, we can arrange the books from greatest number to least number:

This means that the SMALLEST group of books will be the Hardcover Nonfiction books. Thus, we should TEST one of the smaller answers first!

Let's TEST Answer B: 20 books

IF.... Hardcover Nonfiction = 20 Paperback Nonfiction = 40 Paperback Fiction = 80 Total = 20 + 40 + 80 = 140 This is an exact MATCH for what we were told, so this MUST be the answer.