Hi Joy Shaha,

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: B

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

BTGmoderatorDC 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?

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

OA B

Source: Official Guide

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 have:

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 express 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