In a certain classroom, there are 80 books, of which 24 are fiction an

Question

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.

ID: 100113

Bunuel · Accepted Answer

SOLUTION

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?

Given:

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

So, \(x+x+6=24\) --> \(x=9\). Sufficient.

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

So, \(x+x+5=23\) --> \(x=9\). Sufficient.

Answer: D. (Total # of books is redundant information).

Hope it's clear.

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ENGRTOMBA2018 · Answer

The 2X2 matrix is a variation of the venn diagram method and will help you solve the questions correctly and in lesser time than venn diagrams. But for the sake of your question, refer to the attached image for description of the variables. 2016-03-22_19-44-42.jpg Spanish = b+c = 23 Fiction = a+b = 24 Per the question, total books = 80=a+b+c+d (d = not fiction and not Spanish) The question asks us the value of b = ? Per statement 1, a = 6+b ---> clearly sufficient, b=9 Per statement 2, c = 5+b ---> clearly sufficient, b=9 Both statements are sufficient. D is the correct answer. Hope this helps. Learn good strategies to answer questions and not just solving questions blindly.

ziko · Answer

From the first statement: x+(x+6)=24, so x=9 (fiction books written in Spanish).
from st. 2: x+(x+5)=23, x=9 (fiction books written in Spanish)

Both statements separetely suff., so answer D.

I wonder why they provide total number of books (80 books), maybe i am missing something?

gmatrakesh · Answer

Answer is D , as we can use both the statements to arrive at a unique solution

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

total fiction books = 24, so ( x+ x+6 = 24) where x is the fiction books in spanish

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

so x + x+ 5 = 23 , where x is the fiction books in spanish

as we can arrive at a unique solution from both statements alone ... answer is d

vietmoi999 · Answer

IT IS still ven diagram

call x= number of book fiction in spanish

we have 
24-x, x and 23-x

from 1
(24-x) -x=6
we can get x
from 2
(23-x) -x =5
we can get x

oa is d

shekharshrek · Answer

Can some one explain this problem with proper Venn diagram ?

shekharshrek · Answer

Engr2012

Thanks , can you please focus more on the exact meaning of these 2 statements which are highlighted in accordance with the equation above.

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 .

ENGRTOMBA2018 · Answer

Sure, if you look at the venn diagram, statement 1 mentions that "there are 6 more that are not written in Spanish than are written in Spanish"

---> Total fiction books = a+b, fiction + Spanish books = b , fiction and NOT Spanish = a

Thus, per the statement, fiction + NOT Spanish = 6 + (fiction+Spanish) ---> a = 6+b

Similarly, per statement 2, total Spanish books = b+c ---> Spanish ONLY = c and Spanish + fiction = b ---> c=b+5

Hope this helps.

sedgwick · Answer

brunel - I solved this using the table method as well. However, drawing out tables 3x is quite time consuming and I cannot seem to do it in under 3 minutes. Does 3 minutes seem reasonable to you or should I be solving this quicker?

Thanks!

Thanks!

dave13 · Answer

Bunuel

why didnt you use the formulas ?

I mean group 1 +group +2 - both +neither Total = 80 Group 1 is fiction book = 24 Group 2 is spanish book = 23 Both Spanish Fiction = X Neither = 33 80 = 24 +23 - X + 33 why this formula doesnt work ? pushpitkc any idea? i itemized every number memtioned in the question ? what is first right step to tackle overlapping sets ?

pushpitkc · Answer

Hey  dave13

I think when you are told that of the 80 books, 24 are from the genre - Fiction
and 23 of the books are written in Spanish, there could be some books which
are both from the genre fiction and written in Spanish. You are calling that x.
Till here, you are correct!

But how do you come to a conclusion that those books which are neither fiction
nor written in Spanish are 33?

If 23 books are both from the genre fiction and written in Spanish, then there
will be one book which is of the genre Fiction and not written in Spanish. The
remaining books -  56(80 - 23 - 1)  in number fall in neither written in Spanish
nor of the genre fiction.

However, if each of the books written in Spanish is not from the genre Fiction,
there would be  33(80 - 23 - 24)  books which are neither written in Spanish nor 
of the genre fiction

So, basically, the number of books which are neither written in Spanish nor of 
the genre fiction can be between 33 and 56.

Hope this explanation clears your confusion why your method is incorrect.

dave13 · Answer

Hi pushpitkc thanks for your explanation, ok now i understand that neither written in Spanish nor of the genre fiction can be between 33 and 56 --- that means we need to denote Neither as unknown X so i get Total = 80 Group 1 is fiction book = 24 Group 2 is spanish book = 23 Both Spanish Fiction = X Neither = X 80 = 24 +23 - X + X

again doing something wrong ... but what ?

i think i got it... so question is 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. let x be fiction book written in Spanish, then non Spanish fiction books are x+6 neither = y : ? 80= x+x+6.... how to write group 1+group 2 -both + neither ...still dont get

pushpitkc · Answer

Hi  dave13

You will have to have different variables to represent "Neither" and "Both Fiction and Spanish".
The equation will be written as 80 = 23 + 24 + X + Y(which cannot be solved as such)

When you try and solve the first statement, where we are told "Of the fiction books, there are 6 more 
that is not written in Spanish than are written in Spanish" - if we assume the number of fiction books 
that are written in Spanish to be another variable, say "s", the fiction books not written in Spanish are
"s + 6"

Now, we know that the total number of fiction books is 24. 
We can now form the equation s+s+6 = 24 and solving the equation, we get s=9(which is the number of 
fiction books, written in Spanish)

We can now calculate the number of fiction books that are written in Spanish using statement 1 alone. 
Hence, the answer has to be A or D. Similarly, we solve for statement 2 and because the information
given in statement 2 is also enough by itself, we arrive at the solution D!

CEdward · Answer

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.

Let the # of fiction books that are written in Spanish be x.

x + (x + 6) = 24
x = 9 <---- Fiction written in Spanish

Sufficient.

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

Let the # of Spanish books that are fiction be y.

y + (y + 5) = 23 
y = 9 <------ Spanish fiction

Sufficient.

Answer is D.

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=Nr2fssmoK84

kymoll373 · Answer

@Brunuel

Why is no one mentioning the fact that the question does not explicitly state there are only fiction & nonfiction books?

OR did I make a bone head misinterpretation and nonfiction means not fiction, and not the non-fiction book genre.

For Stem 2, I read the verbiage and due to time constraint selected A only due to my perception of the wording in the second stimuli, which I believed could involve a third genre say poetry or whatever

Bunuel · Answer

You're overcomplicating it. The question uses "fiction" and "nonfiction" as two mutually exclusive and collectively exhaustive categories. Nonfiction just means "not fiction," so if a book isn’t fiction, it automatically falls into the nonfiction category. There’s no third type like poetry.

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=hETazLoaUb4 Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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