GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Nov 2019, 12:24

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A certain experimental mathematics program was tried out in 2 classes

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
B
Joined: 15 Sep 2018
Posts: 31
A certain experimental mathematics program was tried out in 2 classes  [#permalink]

Show Tags

New post 20 Sep 2018, 21:29
Since we have at least 2 classes in each of the 32 schools, this means that there will be a total of \(32 \times 2 = 64\) classes in all.

Given that there are 37 teachers, for the first 37 classes, one unique teacher can be assigned to each of the first batch of classes.

This means that if only one teacher is assigned per class, there will be \(64 – 37 = 27\) classes left. So, some of the 37 teachers will have to teach another class[/i][/color] (and possibly more than one).

It’s possible that 27 of the 37 teachers will each teach an additional class. Thus, the least possible number of teachers who will have to teach 3 classes is zero.

To find the maxim number of teachers that could teach 3 classes, we have to add 2 classes to each teacher who is already teaching 1 class. With 27 classes remaining, we have 13 sets of two additional classes, with one left-over class. Thus, the maximum possible number of teachers who could teach 3 classes is 13. This would leave 1 teacher teaching two classes and 23 teachers teaching one class each.

Therefore, the final answer is .
Intern
Intern
User avatar
S
Joined: 07 May 2015
Posts: 41
Location: India
Schools: Darden '21
GPA: 4
CAT Tests
A certain experimental mathematics program was tried out in 2 classes  [#permalink]

Show Tags

New post 14 Oct 2018, 01:36
Bunuel wrote:
A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

A) 0 and 13
B) 0 and 14
C) 1 and 10
D) 1 and 9
E) 2 and 8



32 Schools X 2-Classes each = 64 Classes (in total)
Total no. of teachers = 37

Least no. of teachers who teach 3 classes = 0
[since 2*37=74, can cover up 64 classes]

Greatest no. of teachers who teach 3 classes = 13


Why?
No of Teachers who teach 3 classes = 14
Remaining teachers = 37-14 = 23
No of classes covered = 14*3 = 42
No of remaining classes = 22
Hence we will have a case where one teacher will have no class to teach
Hence, its 13 teachers.
Senior Manager
Senior Manager
avatar
P
Joined: 09 Jun 2014
Posts: 354
Location: India
Concentration: General Management, Operations
Reviews Badge
A certain experimental mathematics program was tried out in 2 classes  [#permalink]

Show Tags

New post 17 Oct 2018, 22:22
1
Bunuel wrote:
A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

A) 0 and 13
B) 0 and 14
C) 1 and 10
D) 1 and 9
E) 2 and 8



An easier way to solve this problem:

1.2 classes in each of 32 schools means total of 2*32=64 classes.
2.Total teachers = 37

Now, MINIMUM value of n(teachers who took three classes)

Suppose all of them 2 classes then 37*2 =74 classes which is more than 64..so we can imagine few taking one classes say 25 people took 2 classes and rest 12 took 1 classes..This means total classe is 64 and value of n=0

Now since we know value of N is 0, eliminate option C,D and E

Now, MAXIMUM value of n(teachers who took three classes)

Focus only on options A and B for which max value is 13 and 14

If you plugin 14 as value of n means 14(teacher)*3=42 classes...classes remaining =64-42=22 and teachers remaning(37-14=23)

So even if one teacher takes one classe we will have an empty class..Hence B is out..

Directly chose A.
Manager
Manager
avatar
B
Joined: 03 Aug 2018
Posts: 66
Location: India
Concentration: Strategy, Operations
GMAT 1: 590 Q45 V26
GPA: 3.5
GMAT ToolKit User
Re: A certain experimental mathematics program was tried out in 2 classes  [#permalink]

Show Tags

New post 22 Oct 2018, 23:33
chetan2u wrote:
Bunuel wrote:
A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

A) 0 and 13
B) 0 and 14
C) 1 and 10
D) 1 and 9
E) 2 and 8


Equation - 64 classes and 37 teachers...

LEAST possible
- all have two so 37*2 = 74, more than 64 classes, so it is possible that NONE of classes had 3 teachers..

GREATEST possible - say x classes have 3 teacher..... so 3x + (37-x) = 64............3x+37-x = 64...............2x = 27................x = 13.5.....
take the INTEGER value as greatest possible = 13

ans 0 and 13..
A


Hi Chetan , thanks for the explanation.

May I ask, why didn't we consider 14 instead of 13 , when your calculation had 13.5 and we aim to increase /look for maximum value ?

Thanks
Abhinav
Intern
Intern
avatar
Joined: 10 Aug 2019
Posts: 2
Location: United States
Schools: NUS '22
GPA: 3.7
Re: A certain experimental mathematics program was tried out in 2 classes  [#permalink]

Show Tags

New post 06 Sep 2019, 21:08
1
a+2b+3c=32*2=64
a+b+c=37

SO b+2c=27
cmin=0,cmax=13
Manager
Manager
avatar
S
Joined: 09 Nov 2015
Posts: 142
A certain experimental mathematics program was tried out in 2 classes  [#permalink]

Show Tags

New post 06 Sep 2019, 23:45
chii has provided a very elegant solution. I am merely elucidating his solution to make it easier to grasp:

The number of teachers teaching one, two and three classes each are 'a', 'b' and 'c' respectively. Thus:

a+b+c=Total # of teachers=37.......(i)
a+2b+3c=Total # of classes=64.....(ii)
Subtracting (i) from (ii), we get:
b+2c=27

Cmin=0 works because, in that case, 27 teachers teach 27*2=54 classes and the other 37-27=10 teachers teach 10*1=10 classes.
For cmax, we have to derive the lowest possible value of 'b'. It can't be 0 because 'c' would then be a fraction. So the least value of 'b' is 1 so the max value of 'c' is 13. So 13 teachers teach 39*3=39 classes, 1 teacher teaches 1*2=2 classes and 23 teachers teach 23*1=23 classes.

ANS:A
GMAT Club Bot
A certain experimental mathematics program was tried out in 2 classes   [#permalink] 06 Sep 2019, 23:45

Go to page   Previous    1   2   [ 26 posts ] 

Display posts from previous: Sort by

A certain experimental mathematics program was tried out in 2 classes

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne