Thabo owns exactly 140 books, and each book is either paperback fictio

Dear AbdurRakib,
I'm happy to help.

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
_________________

Analyse one line at a time:

"Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. "

Total = 140. Say there are x hardcover nonfiction.

"If he owns 20 more paperback nonfiction books than hardcover nonfiction books,"

Paperback nonfiction = 20 + x

"and twice as many paperback fiction books as paperback nonfiction books"

Paperback fiction = 2 * (20 + x) = 40 + 2x

140 = x + (20 + x) + 2 * (20 + x)
4x = 80
x = 20

Answer (B)

140 = paperback fiction (pf) + paperback nonfiction (pn) + hardcover nonfiction (hn)
140 = pf + pn + hn
pn = 20 + hn
pf = 2*pn

hn = ?

140 = pf + pn + hn
140 = 2pn + pn + hn
140 = 3pn + hn
140 = 3 (20 + hn) + hn
hn = 20

F NF TOTAL
P y x+20 x+y+20
H 2y x+20 2y+x+20
TOTAL 3Y 2x+20 140

x+y+20+2y+x+20=140
2x+3y+40=140
2x+3y=100...S1

3Y+2x+20=140


Where am I going wrong?

Dear paidlukkha,
I'm happy to respond.

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.

I also will recommend this post:
Asking Excellent Questions

Does all this make sense?
Mike
_________________

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

P H Total

F 2x+40 0

NF x+20 x

Total 3x+60 x 140

3x + 60 + x = 140
x = 20

Answer (B.)

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:

2n + n + n - 20 = 140

4n = 160

n = 40

Thus, Thabo owns 40 - 20 = 20 hardcover nonfiction books.

Answer: B
_________________

twice as many paperback fiction books as paperback nonfiction books

paperback non fiction= 2 paperback fiction???

A couple of ways to solve this question:

Algebra:



Chart:

Handcover x
Fiction 2(20+x)
Non-fiction 20 + x
Total 140

x + 40 + 2x + 20 + x = 140
x = 20

B

"how many hardcover books nonfiction books does Thabo own?"

What?.. Is this English correct? maybe how many MORE or LESS or something else? There is clearly something missing in the question!

Dear iliavko,

I'm happy to respond.

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
_________________

Hi All,

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:

Paperback Fiction > Paperback Nonfiction > Hardcover Fiction.

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.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Let nos of Hardcover Non Fiction books be x
Then nos of Paperback Non Fictin books will be x+20( as given in question)
So nos of Paperback Fiction books will be 2(x+20)( as given in question)

Sum of all books is 140 as provided in the question
So
x+x+20+2(x+20) = 140
4x+60 =140
4x =80
x =20

Hence No of Hardcover books is 20.
So answer is B

Cheers for a Kudo
_________________

VeritasKarishma - please help

clearly the equation should be x + x+20 + 2x +40 = 140
Hardcover nonfiction = x
Paperback nonfiction = x+20
Paperback fiction = 2(x+20)

However, on my first attempt i did this --which is clearly wrong but i am not able to figure out why
Hardcover nonfiction = x-20
Paperback nonfiction = x
Paperback fiction = 2x

so 2x + x + x-20 = 140

can you tell what's wrong with above eq ?

Hi gmatns2018,

You're "original" set of equations is fine, but it's worth noting that you have made "X" equal the number of Paperback Nonfiction books. That is NOT what the question is asking you to solve for though; the prompt asks for the number of Hardcover Nonfiction books.

Thus, with your original equations, you would end up with X = 40... but again, that is NOT the answer to the question. You have to do one more step: subtract 20 from X to get the number of Hardcover Nonfiction books.

GMAT assassins aren't born, they're made,
Rich

I have attached an image of a double matrix table as a way to approach this question:

Hope this helps.

Tips: I find using double matrix table very useful in questions like this- it is quick and avoids making careless calculation mistakes!

We are asked about the hardcover, non-fiction, so it makes sense to use X

to indicate the element about which we were asked. So let's just call that one X.

If they tell me that there are 20 more paperback, non-fiction than these, well

this is a verbal sentence establishing the ratio of two or more sizes, I need to add to the

smaller quantity. That there are 20 more of these, than these, that means that this

quantity is greater; so this quantity is going to be equal to this quantity +20.

So I added to the small one 20, in order to make it equal to the bigger one.

Same thing here; there are twice as many paperback fiction as paperback non-fiction.

Paperback nonfiction, I know it's X + 20; there are twice as

many these as these, in other words this larger

quantity is going to be equal twice the smaller quantity. At the end of the day, I

know that 2(X + 20) plus this quantity, which is X + 20 plus

the original quantity, which we referred to as an X, equals a 140. This is one

equation with one unknown; should be solvable. 2X + 40 + X + 20 + X =140.

...

4X = 80, so that means that X is equal to a 20 the correct answer is B.

twice as many paperback fiction books as paperback nonfiction books

paperback non fiction= 2 paperback fiction???