OG In a certain classroom, there are 80 books

[AbeNeedsAnswers]

In a certain classroom, there are 80 books, of which 24 are fiction and 23 are written in Spanish. How many of the fiction books are written in Spanish?

(1) Of the fiction books, there are 6 more that are not written in Spanish than are written in Spanish.
(2) Of the books written in Spanish, there are 5 more nonfiction books than fiction books.

D

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Hi AbeNeedsAnswers,

We're told that in a certain classroom, there are 80 books, of which 24 are fiction and 23 are written in Spanish. We're asked for the number of the FICTION books that are written in SPANISH. While this looks like an Overlapping Sets question at first glance, it's actually simpler than that - and you do not need to approach the question in that way to get to the correct answer (some basic arithmetic is all that is needed).

To start, we know that there are 24 fiction books - and SOME of them were written in Spanish. Since only 23 of the 80 books were written in Spanish, no more than 23 of the 24 fiction books could be written in Spanish.

1) Of the fiction books, there are 6 more that are not written in Spanish than are written in Spanish.

We already know that just 24 fiction books are in this classroom - some are written in Spanish and some are NOT. Fact 1 tells us that 6 MORE of those 24 books are NOT written in Spanish than written in Spanish. You can set up a 'System' of equations to determine the number of each, you can 'brute' force the solution or you might recognize that the System exists (so you can avoid doing math altogether). If you do 'do the math', you'd end up with the following equations:

X = fiction books written in Spanish
Y = fiction books NOT written in Spanish
X + Y = 24
Y = X + 6
X=9 and Y=15
Fact 1 is SUFFICIENT

2) Of the books written in Spanish, there are 5 more nonfiction books than fiction books.

Fact 2 can be approached in the same way that Fact 1 is approached:

We already know that just 23 books written in Spanish are in this classroom - some are fiction and some are NOT fiction. Fact 2 tells us that 5 MORE of those 23 books are NOT fiction than fiction. You can set up a 'System' of equations to determine the number of each, you can 'brute' force the solution or you might recognize that the System exists (so you can avoid doing math altogether). If you do 'do the math', you'd end up with the following equations:

B = fiction books written in Spanish
C = NON-fiction books written in Spanish
B + C = 23
C = B + 5
B=9 and C=14
Fact 2 is SUFFICIENT

Final Answer: D

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