Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 30 Jun 2008
Posts: 870

There are 26 students who have read a total of 56 books amon
[#permalink]
Show Tags
28 Sep 2008, 02:27
Question Stats:
40% (01:35) correct 60% (01:41) wrong based on 57 sessions
HideShow timer Statistics
Tere are 26 students who have read a total of 56 books among them. The only books they have read, though, are Aye, Bee, Cod, and Dee. If 10 students have only read Aye, and 8 students have read only Cod and Dee, what is the smallest number of books any of the remaining students could have read?
_________________
"You have to find it. No one else can find it for you."  Bjorn Borg




Magoosh CoFounder
Joined: 17 Sep 2011
Posts: 41
Schools: UC Berkeley (Haas)  Class of 2010

Re: Overlapping sets
[#permalink]
Show Tags
16 Dec 2011, 14:51
One note, we should be careful about wording. I found the original question and it differs slightly from the question posted. The question posted states "only 10 students have read A" This implies that no one else read A except for those 10 students. And it also implies that those 10 students may have read other books. The question source actually states "10 students have only read A", which means that 10 students read book A and nothing else, and others may have also read A. @shinbhu has worked through the problem well. I'll outline a similar approach walking through how I think about the question: 1. We start with 56 books and 26 students. Each student can read up to 4 books: A, B, C, and D. 2.. 10 students only read A. That's 10 students and 10 books. Now we have 46 books and 16 students 3. 8 students read only C and D. That's 8 more students and 16 more books. Now we have 30 books and 8 student remaining. 4. Each of the remaining students can read at most 4 books. But all 8 cannot read 4 books, because that would be 32 books and we only have 30 left. So 7 could read 4 books, and that's 28 books. We still have 1 student and 2 books left. So the minimum number of books a student could read is 2. I hope that helps!
_________________




VP
Joined: 17 Jun 2008
Posts: 1157

Re: PS: Smallest Number of Books
[#permalink]
Show Tags
28 Sep 2008, 03:00
Is it 2?
Since, 18 students have already read a total of 26 books. Thus, remaining 8 students would read the remaining 30 books.
Now, a student can read a maximum of four books. Thus, if seven students read four books each then the eighth student will need to read two books.



Manager
Joined: 22 Sep 2008
Posts: 100

Re: PS: Smallest Number of Books
[#permalink]
Show Tags
29 Sep 2008, 07:44
How it comes total 26 books ?
Have you people consider 8 for C and 8 for D , and 10 for A (10 +8 +8= 26?)
what does "8 students have read only Cod and Dee" mean?
I think we need to take 8 as combine value for Cod and Dee, why we need to take 8 for c and 8 for D
Thanks



VP
Joined: 05 Jul 2008
Posts: 1030

Re: PS: Smallest Number of Books
[#permalink]
Show Tags
29 Sep 2008, 09:36
vr4indian wrote: How it comes total 26 books ?
Have you people consider 8 for C and 8 for D , and 10 for A (10 +8 +8= 26?)
what does "8 students have read only Cod and Dee" mean?
I think we need to take 8 as combine value for Cod and Dee, why we need to take 8 for c and 8 for D
Thanks what does "8 students have read only Cod and Dee" mean? This means 8 students have read 16 books. 10 students have read only Aye This means 10 students read 10 books 18 students read 26 books together 8 students are left with 30 books.



Senior Manager
Joined: 22 Dec 2009
Posts: 253

There are 26 students who have read a total of 56 books..
[#permalink]
Show Tags
14 Feb 2010, 07:41
There are 26 students who have read a total of 56 books among them. The only books they have read, though, are Aye, Bee, Cod, and Dee. If 10 students have only read Aye, and 8 students have read only Cod and Dee, what is the smallest number of books any of the remaining students could have read? Ans: 2 Explanation: According to the problem, 10 students have read only 1 book: Aye, and 8 students have read 2 books: Cod and Dee. This accounts for 18 students, who have read a total of 26 books among them. Therefore, there are 8 students left to whom we can assign books, and there are 30 books left to assign. We can assume that one of these 8 students will have read the smallest possible number if the other 7 have read the maximum number: all 4 books. If 7 students have read 4 books each, this accounts for another 28 books, leaving only 2 for the eighth student to have read. Note that it is impossible for the eighth student to have read only one book. If we assign one of the students to have read only I book, this leaves 29 books for 7 students. This is slightly more than 4 books per students. However, we know that there are only four books available; it is therefore impossible for one student to have read more than four books.
_________________
Cheers! JT........... If u like my post..... payback in Kudos!!  Do not post questions with OAPlease underline your SC questions while postingTry posting the explanation along with your answer choice For CR refer Powerscore CR BibleFor SC refer Manhattan SC Guide ~~Better Burn Out... Than Fade Away~~



CEO
Joined: 17 Nov 2007
Posts: 3061
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: There are 26 students who have read a total of 56 books..
[#permalink]
Show Tags
16 Feb 2010, 09:57
1. initially: 26 students  56 books 2. 10 students read only one book. Other students: 16 students  46 books 3. 8 students read 2 books. Other students: 8 students  30 books. 4. If reminding 8 students read 4 books each, it would be 32 books in total. So, we need to take 2 books from one of students and 2 remains.
_________________
HOT! GMAT Club Forum 2020  GMAT ToolKit 2 (iOS)  The OFFICIAL GMAT CLUB PREP APPs, musthave apps especially if you aim at 700+  Limited Online GMAT/GRE Math tutoring



Manager
Joined: 10 Feb 2010
Posts: 133

Re: There are 26 students who have read a total of 56 books..
[#permalink]
Show Tags
17 Feb 2010, 19:04
2 books
Students  Books  10  10 8  16 ================================== 18  26
Remaining 8 Students, 30 books Smallest by 1 person = 7x4 + 1x2 So, 2 books



Retired Moderator
Joined: 20 Dec 2010
Posts: 1573

Re: There are 26 students who have read a total of 56 books..
[#permalink]
Show Tags
14 Feb 2011, 12:26
I am not too convinced with the explanation; why can't 1 person read 23 of the 30 remaining books and let the rest 7 read 7 different books, 1 each. In that case; the smallest number of books that any of the remaining students reads is going to be 1. And that 1 is just not read by one person; but 7. There are no mandates that a student must read different books. Am I misinterpreting something?
_________________



SVP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1883

Re: 700 level question
[#permalink]
Show Tags
08 Sep 2011, 23:42
If 10 students have read only Aye, and 8 have read only Cod and Dee, the 8 remaining students must: (1) Have read at least Bee (2) Read 30 books among themselves (because of the 56 books, the other 18 students have already read 26) Of the 8 students, 7 can read a maximum of 28 books (i.e. each of the 7 students reads all of Aye, Bee, Cod, and Dee) Therefore the last student may read a minimum of 2 books. The answer is (A)
_________________
GyanOne [www.gyanone.com] Premium MBA and MiM Admissions Consulting
Awesome Work  Honest Advise  Outstanding Results Reach Out, Lets chat!Email: info at gyanone dot com  +91 98998 31738  Skype: gyanone.services



Manager
Joined: 08 Sep 2011
Posts: 51
Concentration: Finance, Strategy

Re: There are 26 students who have read a total of 56 books..
[#permalink]
Show Tags
09 Sep 2011, 12:22
i got 2 after rereading the question. I only 8 once for c and d and not 16. not a bad question just a little tricky on the wording



Intern
Joined: 20 Oct 2011
Posts: 5

Re: There are 26 students who have read a total of 56 books..
[#permalink]
Show Tags
14 Nov 2011, 17:02
fluke wrote: I am not too convinced with the explanation; why can't 1 person read 23 of the 30 remaining books and let the rest 7 read 7 different books, 1 each. In that case; the smallest number of books that any of the remaining students reads is going to be 1. And that 1 is just not read by one person; but 7. There are no mandates that a student must read different books. Am I misinterpreting something? Kind of a confusing question this one, i see your point but I believe that the only books available are Aye, Bee, Cod and Dee. Therefore in order to execute your idea a student would have to repeat the same book several times,... at least this I what I understand from this question... veeery ambiguous I must say.



Intern
Joined: 05 Aug 2011
Posts: 18

There are 26 students who have read a total of 56 books amon
[#permalink]
Show Tags
15 Dec 2011, 08:41
There are 26 students who have read a total of 56 books among them. The only books they have read are A,B,C,D.If only 10 students have read A and 8 students have read only C and D ,what is the smallest number of books any of the remaining students could have read ?
A. 2 B. 4 C. 12 D. 10 E. 5



Manager
Joined: 29 Jul 2011
Posts: 75
Location: United States

Re: Overlapping sets
[#permalink]
Show Tags
15 Dec 2011, 16:21
Let break this down stepbystep, Let B = books, S = students Begin: B = 56, S = 26 10 students read only A, B = 46, S = 16 8 students read C+D, B = 46  (8x2) = 30, S = 16  8 = 8 30 books, 8 students. Lets have the least read person be 8th What is the closest multiple to 30 for the remaining 7 students  7 x 4 = 28. That is 7 students read 4 books each on average. So, 8th read 3028 = 2, which is the least.
_________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS  If negative answer only, still sufficient. No need to find exact solution. PS  Always look at the answers first CR  Read the question stem first, hunt for conclusion SC  Meaning first, Grammar second RC  Mentally connect paragraphs as you proceed. Short = 2min, Long = 34 min



Intern
Joined: 05 Aug 2011
Posts: 18

Re: Overlapping sets
[#permalink]
Show Tags
19 Dec 2011, 05:25
bhavinp wrote: One note, we should be careful about wording. I found the original question and it differs slightly from the question posted.
The question posted states "only 10 students have read A" This implies that no one else read A except for those 10 students. And it also implies that those 10 students may have read other books.
The question source actually states "10 students have only read A", which means that 10 students read book A and nothing else, and others may have also read A. @shinbhu has worked through the problem well. I'll outline a similar approach walking through how I think about the question:
1. We start with 56 books and 26 students. Each student can read up to 4 books: A, B, C, and D. 2.. 10 students only read A. That's 10 students and 10 books. Now we have 46 books and 16 students 3. 8 students read only C and D. That's 8 more students and 16 more books. Now we have 30 books and 8 student remaining. 4. Each of the remaining students can read at most 4 books. But all 8 cannot read 4 books, because that would be 32 books and we only have 30 left. So 7 could read 4 books, and that's 28 books. We still have 1 student and 2 books left. So the minimum number of books a student could read is 2.
I hope that helps! I must have misread the question and posted with the same understanding. Thanks for the explanation.



Magoosh CoFounder
Joined: 17 Sep 2011
Posts: 41
Schools: UC Berkeley (Haas)  Class of 2010

Re: Overlapping sets
[#permalink]
Show Tags
19 Dec 2011, 12:32
No problem! Glad I could help.
_________________



NonHuman User
Joined: 09 Sep 2013
Posts: 13300

Re: There are 26 students who have read a total of 56 books amon
[#permalink]
Show Tags
20 Feb 2019, 00:43
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: There are 26 students who have read a total of 56 books amon
[#permalink]
20 Feb 2019, 00:43






