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# Each of the 45 books on a shelf is written

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Intern
Joined: 25 Jun 2015
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Schools: ISB '18
Each of the 45 books on a shelf is written  [#permalink]

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23 Dec 2015, 14:16
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Difficulty:

75% (hard)

Question Stats:

53% (01:43) correct 47% (01:54) wrong based on 1246 sessions

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Q# 121 OG. Quant Review 2016

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback.
If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a
paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperback.
(2) Of the books on the shelf, 15 are written in Spanish.

Need help to solve this one.
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Joined: 02 Aug 2009
Posts: 8023
Re: Each of the 45 books on a shelf is written  [#permalink]

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23 Dec 2015, 22:55
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ajayvyavahare wrote:
Q# 121 OG. Quant Review 2016

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback.
If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a
paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperback.
(2) Of the books on the shelf, 15 are written in Spanish.

Need help to solve this one.

hi,
is overall prob given for paperback+spanish <1/2..
1) 30 out of 45 are paperbeck..
if all 30 are spanish too... prob>1/2..
if none of them is spanish.. prob=0<1/2..
no info ..insuff

2) 15 out of 45 are written inspanish...
if we take all as paperback.. prob =15/45=1/3, which is less than 1/2..
so at the best scenario too, the prob <1/2.. suff
ans B
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Re: Each of the 45 books on a shelf is written  [#permalink]

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23 Dec 2015, 14:49
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ajayvyavahare wrote:
Q# 121 OG. Quant Review 2016

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback.
If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a
paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperback.
(2) Of the books on the shelf, 15 are written in Spanish.

Need help to solve this one.

Refer to the attached picture for explanation.

Per the question, 45 books are on a shelf. You need to find whether the probability of picking a Spanish paperback is <1/2 --> In other words, is the number of Spanish paperback books <22.5 (=22 as the books can not 0.5!)

Per statement 1, 30 are paperback. Look at 2nd table in the attached figure. The maximum number of Spanish paperback books can be = 30 , giving us a "no" to the question asked but if the same paperback books are lets say = 10, then you get "yes" for the question asked. Thus this statement is NOT sufficient.

Per statement 2, refer to the 3rd table, you can clearly see that the maximum Spanish paperback books can be 15, thus giving us a definite "yes" to the question asked. Hence this statement is sufficient.

Hope this helps.
Attachments

12-23-15 4-45-21 PM.jpg [ 61.49 KiB | Viewed 13709 times ]

##### General Discussion
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Re: Each of the 45 books on a shelf is written  [#permalink]

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17 May 2016, 03:06
chuckkkkk wrote:
Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is
either a hardcover book or a paperback. If a book is to be selected at random from the books
on the shelf, is the probability less than 1/2 that the book selected will be a paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperbacks.
(2) Of the books on the shelf, 15 are written in Spanish.

The maximum number of books that can be written in Spanish ( irrespective of whether its hardcover or paperback) is 15 as per option 2
So, lets say all spanish books are ppaerbacks ,then whats the probability ?? 15/45 i.e 1/3 <1/2
Hence B

For option A , we can't specifically determine how many spanish books are there
Hence insufficent
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Re: Each of the 45 books on a shelf is written  [#permalink]

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17 May 2016, 16:39
This is a 2 by 2 question that frequently appears in the GMAT Math.

Looking at the attachment, the question, if we modify, is d/45<1/2?, d<45/2=22.5?. Looking at the condition 1), we get d=15<22.5. The answer is yes and the condition is sufficient. Hence, the correct answer is B.

- Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
Attachments

3.jpg [ 23.41 KiB | Viewed 12864 times ]

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Re: Each of the 45 books on a shelf is written  [#permalink]

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17 Jan 2018, 11:52
AJ1012 wrote:
Q# 121 OG. Quant Review 2016

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback.
If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a
paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperback.
(2) Of the books on the shelf, 15 are written in Spanish.

Need help to solve this one.

Is there any further explanation on this? Not convinced at all on the OA.
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Re: Each of the 45 books on a shelf is written  [#permalink]

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19 Jan 2018, 06:59
Shenaz wrote:
AJ1012 wrote:
Q# 121 OG. Quant Review 2016

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback.
If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a
paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperback.
(2) Of the books on the shelf, 15 are written in Spanish.

Need help to solve this one.

Is there any further explanation on this? Not convinced at all on the OA.

Hi

Did you go through this solution:
https://gmatclub.com/forum/each-of-the- ... l#p1621801

Basically, as per second statement, only 15 books are in Spanish (15 is obviously less than half of 45). Even if all these Spanish books are paperback, then the probability of selecting a paperback Spanish book will be 15/45 = 1/3 which is < 1/2. And if some Spanish books are hardcover also, then the probability of selecing a Spanish paperback will be even lesser than 1/3 (so definitely lesser than 1/2). So, as per second statement, probability of picking a paperback Spanish book will always be < 1/2. That's why the answer is B.
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Re: Each of the 45 books on a shelf is written  [#permalink]

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01 Feb 2019, 18:02
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Re: Each of the 45 books on a shelf is written   [#permalink] 01 Feb 2019, 18:02
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