Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 25 Jun 2015
Posts: 6

Each of the 45 books on a shelf is written
[#permalink]
Show Tags
23 Dec 2015, 14:16
Question Stats:
54% (01:15) correct 46% (01:19) wrong based on 576 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Aug 2009
Posts: 6802

Re: Each of the 45 books on a shelf is written
[#permalink]
Show Tags
23 Dec 2015, 22:55
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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




Current Student
Joined: 20 Mar 2014
Posts: 2638
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Each of the 45 books on a shelf is written
[#permalink]
Show Tags
23 Dec 2015, 14:49
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. B is the correct answer. Hope this helps.
Attachments
122315 44521 PM.jpg [ 61.49 KiB  Viewed 7501 times ]




Manager
Joined: 24 Jun 2014
Posts: 50
Concentration: Social Entrepreneurship, Nonprofit

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



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GPA: 3.82

Re: Each of the 45 books on a shelf is written
[#permalink]
Show Tags
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 6675 times ]
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 16 May 2016
Posts: 8

Re: Each of the 45 books on a shelf is written
[#permalink]
Show Tags
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. Please help



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1343
Location: India

Re: Each of the 45 books on a shelf is written
[#permalink]
Show Tags
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. Please help Hi Did you go through this solution: https://gmatclub.com/forum/eachofthe ... l#p1621801Basically, 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.




Re: Each of the 45 books on a shelf is written &nbs
[#permalink]
19 Jan 2018, 06:59






