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A bookstore stocks of its books as fiction works, and less t

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A bookstore stocks of its books as fiction works, and less t [#permalink] New post   24 Feb 2020, 05:40
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A bookstore stocks of its books \(\frac{1}{5}\) as fiction works, and \(\frac{1}{3}\) less than the fiction books as self-help books. What fraction of the total books are the fiction and self-help books?

A. \(\frac{3}{5}\)

B. \(\frac{11}{30}\)

C. \(\frac{4}{15}\)

D. \(\frac{2}{15}\)

E. \(\frac{1}{3}\)

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rishabhrbs96
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Re: A bookstore stocks of its books as fiction works, and less t [#permalink] New post   12 May 2020, 10:10
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Let total books be x.

number of fiction books = x/5

self-help books are 1/3 less than the fiction books,
=> number of self-help books = x/5 - (1/3)*(x/5) = (2/3)*(x/5)

so, their sum is = x/5 + (2/3)*(x/5)
= (x/5)*[1 +(2/3)]
= (x/5)*(5/3)
= x/3
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Re: A bookstore stocks of its books as fiction works, and less t [#permalink] New post   29 Aug 2021, 05:46
rishabhrbs96 wrote:
Let total books be x.

number of fiction books = x/5

self-help books are 1/3 less than the fiction books,
=> number of self-help books = x/5 - (1/3)*(x/5) = (2/3)*(x/5)

so, their sum is = x/5 + (2/3)*(x/5)
= (x/5)*[1 +(2/3)]
= (x/5)*(5/3)
= x/3


When calculating the number of self-help books why did you did x/5 - (1/3)*(x/5) and not x/5 - (1/3). It just says 1/3 less than the fiction books so this seems valid to me. But I couldn't get the correct answer. What am I missing?
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A bookstore stocks of its books as fiction works, and less t [#permalink] New post   29 Aug 2021, 08:16
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Hey,

So you missed out on wordings.
\(\frac{1}{3}\) less than the fiction books means that the self-help books are \(\frac{2}{3}\) of the fiction books.

For ex.
Let's say fiction books are \(60\). So self-help books = \((1 - \frac{1}{3}) * 60 = \frac{2}{3}* 60 = 40\)

Please ask if the doubt remains.

koala wrote:

When calculating the number of self-help books why did you did x/5 - (1/3)*(x/5) and not x/5 - (1/3). It just says 1/3 less than the fiction books so this seems valid to me. But I couldn't get the correct answer. What am I missing?
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koala
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Re: A bookstore stocks of its books as fiction works, and less t [#permalink] New post   30 Aug 2021, 05:41
rx10 wrote:
Hey,

So you missed out on wordings.
\(\frac{1}{3}\) less than the fiction books means that the self-help books are \(\frac{2}{3}\) of the fiction books.

For ex.
Let's say fiction books are \(60\). So self-help books = \((1 - \frac{1}{3}) * 60 = \frac{2}{3}* 60 = 40\)

Please ask if the doubt remains.

koala wrote:

When calculating the number of self-help books why did you did x/5 - (1/3)*(x/5) and not x/5 - (1/3). It just says 1/3 less than the fiction books so this seems valid to me. But I couldn't get the correct answer. What am I missing?


Understood. Thanks!
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Re: A bookstore stocks of its books as fiction works, and less t [#permalink] New post   30 Aug 2021, 06:05
simple soln:

Let total books be 15, 1/5th of total books is fiction that makes it 3
For self help books it becomes: 3 - (1/3) *3 = 3-1 = 2

Therefore 3 + 2 = 5
Ans : 5/15 equals 1/3
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Re: A bookstore stocks of its books as fiction works, and less t [#permalink]
30 Aug 2021, 06:05
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