greatest possible numberand the least possible number!!!

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apoorva.srivastva: Master | Next Rank: 500 Posts; Posts: 146; Joined: Wed Aug 27, 2008 5:41 am; Thanked: 3 times

greatest possible numberand the least possible number!!!

by apoorva.srivastva » Sat Jan 16, 2010 10:27 am

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If 37 teachers are to be assigned to 64 classes in such a way that each of teacher
teaches at least one class and at most three classes. What are the greatest possible numberand the least possible number of the teachers who teach three classes?
(A) 14,0
(B) 13, 1
(C) 13, 0
(D) 12, 2
(E) 12, 1

OA is C

explain for the greatest!!

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Source: Beat The GMAT — Problem Solving | Sat Jan 16, 2010 10:27 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 16, 2010 1:09 pm

apoorva.srivastva wrote:If 37 teachers are to be assigned to 64 classes in such a way that each of teacher
teaches at least one class and at most three classes. What are the greatest possible numberand the least possible number of the teachers who teach three classes?
(A) 14,0
(B) 13, 1
(C) 13, 0
(D) 12, 2
(E) 12, 1

OA is C

explain for the greatest!!

For the greatest, first assign 1 class to each teacher (to satisfy that condition)
We now have 27 classes remaining to assign.
To maximize the number of teachers who get 3 classes, start giving 2 additional classes to each teacher.
We have 27 classes to distribute, and we are giving each teacher 2 additional classes. We can do this 13 (and 1/2

) times.
We now have 13 teachers with 3 classes.

Brent Hanneson - Creator of GMATPrepNow.com

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apoorva.srivastva: Master | Next Rank: 500 Posts; Posts: 146; Joined: Wed Aug 27, 2008 5:41 am; Thanked: 3 times

by apoorva.srivastva » Sat Jan 16, 2010 1:23 pm

thanks brent!! :)
simply awesome!!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Sep 24, 2019 2:24 pm

apoorva.srivastva wrote:If 37 teachers are to be assigned to 64 classes in such a way that each of teacher
teaches at least one class and at most three classes. What are the greatest possible numberand the least possible number of the teachers who teach three classes?
(A) 14,0
(B) 13, 1
(C) 13, 0
(D) 12, 2
(E) 12, 1

OA is C

explain for the greatest!!

Let a, b, and c be the number of teachers who teach exactly one class, two classes, and three classes, respectively. We can create the equations:

a + b + c = 37

and

a + 2b + 3c = 64

Since 64/3 = 21 R 1, we see that c â‰¤ 21. However, by looking at the answer choices, we can see that c is actually much less than 21. So let's start with c = 14.

If c = 14, the two equations above reduce to a + b = 23 and a + 2b = 22, respectively. However, we see that this is not possible since the value of a + b can't be more than the value of a + 2b.

Now let's try c = 13.

If c = 13, the two equations reduce to a + b = 24 and a + 2b = 25, respectively. We see that this is possible since a = 23 and b = 1 would satisfy both equations.

So 13 is the maximum value of c. Let's now determine the minimum value of c. If c = 0, then we have a + b = 37 and a + 2b = 64. We see that this is possible since a = 10 and b = 27 would satisfy both equations.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
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