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Each of the 45 books on a shelf is written either in English or in Spa
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23 Dec 2015, 13:16
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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.
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 _________________
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.
Re: Each of the 45 books on a shelf is written either in English or in Spa
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17 May 2016, 02:06
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.
I don't get the answer, could someone please explain, thanks.
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
Re: Each of the 45 books on a shelf is written either in English or in Spa
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17 May 2016, 15:39
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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.
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. Please help
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. Please help
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.
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
Just a small correction , for statement 1) we can’t take none case bcz each book is either written in English or Spanish and each book is either a paperback or hardcover !!
We can take the last numbers like 1,2 instead of taking 0
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.
Given: 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. A book is to be selected at random from the books on the shelf.
Target question:Is the probability less than 1/2 that the book selected will be a paperback written in Spanish? This is a good candidate for rephrasing the target question
Let's use the Double Matrix Method to solve this question. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of books, and the two characteristics are: - English or Spanish - Hardcover or paperback
We can set up our diagram like this:
1/2 of 45 = 22.5 So in order for the probability to be less than 1/2, we need 22 or fewer books to be Spanish paperbacks. In other words, we need 22 or fewer books in the yellow shaded region. Let's use this information to REPHRASE the target question REPHRASED target question:Is the number of books in the yellow shaded region 22 or less?
Statement 1: Of the books on the shelf, 30 are paperback If 30 of the 45 books are paperback, then the remaining 15 books must be hardcover. We'll add this to our diagram
There are many different ways to complete this diagram so that we meet the given conditions. For example, we could have the following situation:
In this case, the answer to the REPHRASED target question is YES, the number of books in the yellow shaded region IS 22 or less
Alternatively, we could also have this situation:
In this case, the answer to the REPHRASED target question is NO, the number of books in the yellow shaded region is NOT 22 or less
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Of the books on the shelf, 15 are written in Spanish. When we add this information to our diagram, we get:
IMPORTANT: This tells us that the two boxes in the bottom row, must add to 15. So it will be impossible for the value in the yellow shaded region to be greater than 22. In other words, the answer to the REPHRASED target question is YES, the number of books in the yellow shaded region IS 22 or less Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video:
Cheers, Brent _________________
If you enjoy my solutions, I think you'll like my GMAT prep course.
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.
I have a doubt - As per stmt 2, if we say all 45 are paperback, then probability is 1/3; However, if we say 30 are paperback, wouldn't probability be 1/2, or for that matter 15 are paperback, wouldn't it make probability as 1 ?? Why shouldn't the answer be 'C'
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.
I have a doubt - As per stmt 2, if we say all 45 are paperback, then probability is 1/3; However, if we say 30 are paperback, wouldn't probability be 1/2, or for that matter 15 are paperback, wouldn't it make probability as 1 ?? Why shouldn't the answer be 'C'
Hello Anurag,
It seems like you have misinterpreted the question. The question is not about the probability of picking a Spanish paperback OF all the paperbacks. The question asks us if the probability of picking a “Paperback written in Spanish” is less than ½ when ANY book is selected at random. There’s as big a difference between the two as chalk from cheese.
This is a very common problem that many GMAT test takers face. They end up solving a drastically different question in their head when they have to actually solve the question they see on the screen. Look at the table given below:
The question says “If a BOOK is selected at random”. This means your sample space is 45 (the cell highlighted in Green) and hence should be in the denominator. Whereas, the question that YOU solved in your head is “If a paperback is selected at random”. This means YOUR sample space was the cell highlighted in red, which is of course wrong. I hope that clarifies your doubt.
Look at how many Spanish books are there in total, as per Statement II (the cell highlighted in blue). If there are 15 books of Spanish in total, there would be either 15 paperbacks or lesser. (the cell highlighted in yellow) \(\frac{15}{45}\) is definitely less than ½. We can answer the question with a definite NO which is an accepted answer on a YES-NO type of DS question.
This is another common mistake I have seen test takers making on a YES-No type of DS question – forgetting that a NO is as good as a YES. Since statement II alone is sufficient to give us a NO, the correct answer option is B.
Here’s a link to one of our articles on Data Sufficiency for your reference. This will really help you to not make such errors on a DS question. https://bit.ly/348ndXx
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.
I have a doubt - As per stmt 2, if we say all 45 are paperback, then probability is 1/3; However, if we say 30 are paperback, wouldn't probability be 1/2, or for that matter 15 are paperback, wouldn't it make probability as 1 ?? Why shouldn't the answer be 'C'
Hello Anurag,
It seems like you have misinterpreted the question. The question is not about the probability of picking a Spanish paperback OF all the paperbacks. The question asks us if the probability of picking a “Paperback written in Spanish” is less than ½ when ANY book is selected at random. There’s as big a difference between the two as chalk from cheese.
This is a very common problem that many GMAT test takers face. They end up solving a drastically different question in their head when they have to actually solve the question they see on the screen. Look at the table given below:
Attachment:
03rd Apr 2020 - Reply 1.jpg
The question says “If a BOOK is selected at random”. This means your sample space is 45 (the cell highlighted in Green) and hence should be in the denominator. Whereas, the question that YOU solved in your head is “If a paperback is selected at random”. This means YOUR sample space was the cell highlighted in red, which is of course wrong. I hope that clarifies your doubt.
Look at how many Spanish books are there in total, as per Statement II (the cell highlighted in blue). If there are 15 books of Spanish in total, there would be either 15 paperbacks or lesser. (the cell highlighted in yellow) \(\frac{15}{45}\) is definitely less than ½. We can answer the question with a definite NO which is an accepted answer on a YES-NO type of DS question.
This is another common mistake I have seen test takers making on a YES-No type of DS question – forgetting that a NO is as good as a YES. Since statement II alone is sufficient to give us a NO, the correct answer option is B.
Here’s a link to one of our articles on Data Sufficiency for your reference. This will really help you to not make such errors on a DS question. https://bit.ly/348ndXx
Hope that helps!
Hi Aravind,
Thanks a lot for detailed explanation. It cleared my doubt. Thanks again.
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