February 20, 2019 February 20, 2019 08:00 PM EST 09:00 PM EST Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
Author 
Message 
TAGS:

Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4486

John has on his shelf four books of poetry
[#permalink]
Show Tags
09 Jan 2013, 14:15
Question Stats:
90% (01:45) correct 10% (01:58) wrong based on 209 sessions
HideShow timer Statistics
John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work? (A) 1/2 (B) 2/5 (C) 3/10 (D) 7/20 (E) 8/45For a full discussion of probability and counting questions, as well as a complete solution to this question, see: http://magoosh.com/gmat/2013/gmatproba ... echniques/Mike
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Senior Manager
Joined: 27 Jun 2012
Posts: 369
Concentration: Strategy, Finance

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
09 Jan 2013, 14:42
You can choose 1 Novel book and 1 Reference work in two ways: If you choose Novel first and then Reference > Probability \(P1 = \frac{4}{10} * \frac{2}{9} = \frac{8}{90}\) If you choose Reference first and then Novel > Probability \(P2 = \frac{2}{10} * \frac{4}{9} = \frac{8}{90}\) Probability(1 novel and 1 reference work) = \(P1 + P2 = \frac{8}{90}+\frac{8}{90}= \frac{8}{45}.\) Hence choice (E)
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Finance your Student loan through SoFi and get $100 referral bonus : Click here



Manager
Joined: 18 Oct 2011
Posts: 86
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01302013
GPA: 3.3

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
10 Jan 2013, 07:52
(4C2 * 2C2) / (10C2)
8/45. E



Manager
Joined: 30 Mar 2013
Posts: 108

John has on his shelf four books of poetry
[#permalink]
Show Tags
19 Sep 2014, 10:27
hello, Why can't we do it this way: 4/10 *2/9= 4/45? And if we are multiplying by 2 to change the order, then why didn't we do the same for this question: adivisionofacompanyconsistsofsevenmenandfivewomen145433.htmlHere we used the same approach: 5/12 * 4/11 = 5/33. I'm very confused why the first question has been multiplied by two and not this one as well. After all, there are two ways of picking the women too.



Intern
Joined: 28 Mar 2014
Posts: 4

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
12 Oct 2014, 10:18
usre123 wrote: hello, Why can't we do it this way: 4/10 *2/9= 4/45? And if we are multiplying by 2 to change the order, then why didn't we do the same for this question: adivisionofacompanyconsistsofsevenmenandfivewomen145433.htmlHere we used the same approach: 5/12 * 4/11 = 5/33. I'm very confused why the first question has been multiplied by two and not this one as well. After all, there are two ways of picking the women too. This is because this question asks us to pick two separate books. If the question asked us the probability to pick 2 novels then you wouldn't multiply with 2. Similarly, the question you are referring to asks you the probability of picking 2 women. Therefore you don't multiply by 2. Had it asked you the probability of picking one man and one woman then you would multiply by 2 because you could pick the man first or pick the man second. When you pick only women, it doesn't matter what's first or second because they both are women. Hope that helps!



Manager
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
WE: Analyst (Commercial Banking)

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
05 Nov 2014, 10:23
I agree with one of the above posters. I think the correct answer should 4/5. Once we pick a book, it's no longer on the shelf. So (4/10) * (2/9) = 4/45
incorrect?



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
06 Nov 2014, 05:14
JackSparr0w wrote: John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work? (A) 1/2 (B) 2/5 (C) 3/10 (D) 7/20 (E) 8/45
I agree with one of the above posters. I think the correct answer should 4/5. Once we pick a book, it's no longer on the shelf. So (4/10) * (2/9) = 4/45
incorrect? When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/10*2/9 + 2/10*4/9 = 8/45. Answer: E. Or, use combinations: \(P=\frac{C^1_4*C^1_2}{C^2_{10}}=\frac{8}{45}\). Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 10 Mar 2013
Posts: 498
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
05 Jul 2015, 02:57
Hi everyone here's the shortest way to tackle such questions  Probability approach Total = 10 Books 4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Math Expert
Joined: 02 Aug 2009
Posts: 7334

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
05 Jul 2015, 03:17
BrainLab wrote: Hi everyone here's the shortest way to tackle such questions  Probability approach Total = 10 Books
4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick hi, your answer is correct but approach is wrong... how did you get 4 as numerator in both cases .. reference books are o two in number so it should be 2/9.. so to pick up two books randomly ans is 4/10*2/9, but these two books can be picked up in 2! ways within themselves.. so 4/10*2/9*2!=8/45..
_________________
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 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Senior Manager
Joined: 10 Mar 2013
Posts: 498
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

John has on his shelf four books of poetry
[#permalink]
Show Tags
05 Jul 2015, 03:23
chetan2u wrote: BrainLab wrote: Hi everyone here's the shortest way to tackle such questions  Probability approach Total = 10 Books
4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick hi, your answer is correct but approach is wrong... how did you get 4 as numerator in both cases .. reference books are o two in number so it should be 2/9.. so to pick up two books randomly ans is 4/10*2/9, but these two books can be picked up in 2! ways within themselves.. so 4/10*2/9*2!=8/45.. The second 4 in the numerator is YOUR 2! ... you can write it 2/9*2 or 4/9 I should have written it down in a more detailed way.. just too involved in such kind of questions in the last time.. that's why skipping some basic steps... ))
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Math Expert
Joined: 02 Aug 2009
Posts: 7334

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
05 Jul 2015, 04:26
BrainLab wrote: chetan2u wrote: BrainLab wrote: Hi everyone here's the shortest way to tackle such questions  Probability approach Total = 10 Books
4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick hi, your answer is correct but approach is wrong... how did you get 4 as numerator in both cases .. reference books are o two in number so it should be 2/9.. so to pick up two books randomly ans is 4/10*2/9, but these two books can be picked up in 2! ways within themselves.. so 4/10*2/9*2!=8/45.. The second 4 in the numerator is YOUR 2! ... you can write it 2/9*2 or 4/9 I should have written it down in a more detailed way.. just too involved in such kind of questions in the last time.. that's why skipping some basic steps... )) hi, you did mention about denominator 10 and 9, so expected that you will not miss out mentioning about my 2! , after all it is more likely to be missed by students than 9 in denominator..i know 2/9 * 2! is 4/9, but it is important to understand the reasoning behind it.. otherwise you could have straight way written 8/45 , after all it is equal to 4/10*4/9... Anyway good shortest way to answer such Qs
_________________
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 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Current Student
Joined: 24 Oct 2014
Posts: 48
Location: United Arab Emirates
GPA: 3.56

John has on his shelf four books of poetry
[#permalink]
Show Tags
19 Aug 2016, 13:17
BrainLab wrote: chetan2u wrote: BrainLab wrote: Hi everyone here's the shortest way to tackle such questions  Probability approach Total = 10 Books
4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick hi, your answer is correct but approach is wrong... how did you get 4 as numerator in both cases .. reference books are o two in number so it should be 2/9.. so to pick up two books randomly ans is 4/10*2/9, but these two books can be picked up in 2! ways within themselves.. so 4/10*2/9*2!=8/45.. The second 4 in the numerator is YOUR 2! ... you can write it 2/9*2 or 4/9 I should have written it down in a more detailed way.. just too involved in such kind of questions in the last time.. that's why skipping some basic steps... )) Sorry, but both of you sound off in your approach to this. The second 2 in the numerator appears because you need to account for the order in which you end up picking. i.e. p(novel) x p(ref) + p(ref) x p(novel) (4/10 x 2/9) + (2/9 x 4/10) or (4/10 x 2/9) x 2! This is not the same as 4/10 x (2/9 x 2!)



Intern
Joined: 01 Apr 2015
Posts: 20
Location: United States

John has on his shelf four books of poetry
[#permalink]
Show Tags
17 Dec 2017, 08:46
nyoebic wrote: usre123 wrote: hello, Why can't we do it this way: 4/10 *2/9= 4/45? And if we are multiplying by 2 to change the order, then why didn't we do the same for this question: http://gmatclub.com/forum/adivisionof ... 45433.htmlHere we used the same approach: 5/12 * 4/11 = 5/33. I'm very confused why the first question has been multiplied by two and not this one as well. After all, there are two ways of picking the women too. This is because this question asks us to pick two separate books. If the question asked us the probability to pick 2 novels then you wouldn't multiply with 2. Similarly, the question you are referring to asks you the probability of picking 2 women. Therefore you don't multiply by 2. Had it asked you the probability of picking one man and one woman then you would multiply by 2 because you could pick the man first or pick the man second. When you pick only women, it doesn't matter what's first or second because they both are women. Hope that helps! I'm still not sure I understand the logic here. We multiply by 2, which increases the probability that the event would occur. Why would the probability be higher (double) when we pick one book from two different genres, rather than picking two books from one genre? At the end of the day, we are still picking two books. In other words, why would the probability of picking one of one type of book and one of another type of book be higher than the probability of picking two of one type of book? As Usre123 mentioned, we can still pick those two books of the same genre in two different orders. Please help me understand the logic here  thanks!



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4486

Re: John has on his shelf four books of poetry
[#permalink]
Show Tags
18 Dec 2017, 13:30
mbah191 wrote: I'm still not sure I understand the logic here. We multiply by 2, which increases the probability that the event would occur. Why would the probability be higher (double) when we pick one book from two different genres, rather than picking two books from one genre? At the end of the day, we are still picking two books. In other words, why would the probability of picking one of one type of book and one of another type of book be higher than the probability of picking two of one type of book? As Usre123 mentioned, we can still pick those two books of the same genre in two different orders. Please help me understand the logic here  thanks! Dear mbah191, This is Mike McGarry, author of the question. I'm happy to respond. The curious thing about this question is that, for the purpose of the question, all we know is that we have " four books of poetry, four novels, and two reference works." In other words, for the purpose of the question, we are considering the four books of poetry identical, the four novels identical, and the two reference works identical. This may or may not be the case with the real books, but this is how the problem is set up. Let's pretend that all these books in each of the three categories are identical. Suppose, for some reason, John has four identical copies of the same poetry book, four identical copies of the same novel, and two identical copies of the same dictionary. The only way to arrive at the result of "two poetry books" would be to pick a poetry book on the first choice and another poetry book on the second choice. There's no other way to reach that result. By contrast, to get the result "one novel and one reference book," it's possible to get to that result in two different ways: (1) pick a novel first, then pick a reference work on the second choice (2) pick a reference work first, then pick a novel on the second choice Unlike the twoofthesame case, there are two different routes that lead to this same result. If we figure out the probability of following one of these routes, we would have to double that probability to account for all the ways to arrive at that result. Does all this make sense? Mike
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)




Re: John has on his shelf four books of poetry
[#permalink]
18 Dec 2017, 13:30






