Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jun 0205:30 AM PDT
-07:30 AM PDT
Ready to master GMAT Data Insights? Get empowered with smart strategies to conquer Data Sufficiency questions with confidence and ease! Learn the secrets to solving these questions with precision and efficiency.
Jun 0211:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.- Jun 02
01:30 PM IST
-11:30 PM IST
With brand new features like:AI-driven Planner tool, 850+ data Insights practice questions and GMAT Focus Edition Adaptive mock tests with ESR+ analysis and personal mentor support, our course is the most comprehensive course for GMAT Focus Edition. 
Jun 0105:30 AM PDT
-07:30 AM PDT
Struggling with shuffling between multiple data sets and question choices? With DI scores now equally weighted, learn how to reduce solving time and boost accuracy on these questions through clever data set analysis. Join us for expert tips!
Jun 0608:00 PM PDT
-09:00 PM PDT
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Jun 0712:00 PM PDT
-01:00 PM PDT
In this GMAT experience talk show, we talk to Tavishi, a young MBA aspirant from India who recently scored 725 in her latest GMAT Focus exam. It’s a 99.9 percentile score on the new GMAT Focus edition and she achieved this feat in her first GMAT attempt.- Jun 11
05:30 AM PDT
-12:00 PM PDT
Register for the GMAT Club Virtual MBA Spotlight fair, the biggest MBA fair of the year. You will have a chance to hear Admissions directors from almost every Top 20 program speak, network with peers, and more.
A shelf contains 20 different books of which 4 are in single volume an
[#permalink]
10 Feb 2021, 09:30
10 Feb 2021, 09:30
1
Kudos
5
Bookmarks
Expert Reply
Show timer
00:00
A
B
C
D
E
Difficulty:
95%
(hard)
Question Stats:
18% (01:44) correct
82%
(01:43)
wrong
based on 55
sessions
A shelf contains 20 different books of which 4 are in single volume and the others form sets of 8, 5 and 3 volumes respectively. Number of ways in which the books may be arranged on the shelf, if the volumes of each set are together and in their due order is
(A) \(\frac{20!}{8!5!3!}\)
(B) 7!
(C) 8!
(D) 7*8!
(D) 9!
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) \(\frac{20!}{8!5!3!}\)
(B) 7!
(C) 8!
(D) 7*8!
(D) 9!
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
Re: A shelf contains 20 different books of which 4 are in single volume an
[#permalink]
10 Feb 2021, 23:07
10 Feb 2021, 23:07
3
Kudos
2
Bookmarks
Expert Reply
Bunuel wrote:
A shelf contains 20 different books of which 4 are in single volume and the others form sets of 8, 5 and 3 volumes respectively. Number of ways in which the books may be arranged on the shelf, if the volumes of each set are together and in their due order is
(A) \(\frac{20!}{8!5!3!}\)
(B) 7!
(C) 8!
(D) 7*8!
(D) 9!
(A) \(\frac{20!}{8!5!3!}\)
(B) 7!
(C) 8!
(D) 7*8!
(D) 9!
So what do we have in 20 books : \(A, B, C, D, (E_1, E_2...E_8), (F_1, F_2....F_5), (G_1, G_2, G_3)\)
Now, as all the volumes of a book are together and in due order, we can take \((E_1, E_2...E_8), (F_1, F_2....F_5), (G_1, G_2, G_3)\) as \(E_{(1-8)}, \ \ F_{(1-5)} \ \ G_{(1-3)}\)
Thus we have 7 books : \(A, B, C, D, E_{(1-8)}, \ \ F_{(1-5)} \ \ G_{(1-3)}\). These can be arranged in 7! ways.
Now, due order could mean ascending order or descending order, that is it could be \(E_{(1-8)}, \ \ or \ \ E_{(8-1)}\), so each of sets of E, F and G can be arranged in 2 ways each.
Answer = 7!*2*2*2=8*7!=8!
C
General Discussion
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Given Kudos: 91
Q51 V47
Re: A shelf contains 20 different books of which 4 are in single volume an
[#permalink]
17 Apr 2022, 09:31
17 Apr 2022, 09:31
2
Kudos
Expert Reply
Bunuel wrote:
A shelf contains 20 different books of which 4 are in single volume and the others form sets of 8, 5 and 3 volumes respectively. Number of ways in which the books may be arranged on the shelf, if the volumes of each set are together and in their due order is
The problem with the question is that the phrase "in their due order" is just not something anyone says in English, so there's no way to guess what it means. I imagine Chetan above has guessed the question designer's intention, but I've never seen a set of books arranged "in order" where the books went, from left to right, Volume 3, Volume 2, then Volume 1. I would assume here that the sets of books are arranged Volume 1, Volume 2, and Volume 3 from left to right. And if that's what we're doing, we really just have seven books (four individual books, and three sets that are in a fixed order) and the answer is 7!.
If the question means something else, it needs to be worded differently, because there's no way to guess the answer should be 8! here.
