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

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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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.




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.
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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?

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

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

Can some one explain this problem with proper Venn diagram ?

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.

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.
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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!

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 ?

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.

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

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!

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.
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Answer: Option D

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