It is currently 19 Mar 2018, 20:59

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# At a certain university, the ratio of the number of teaching

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 Jun 2008
Posts: 45
At a certain university, the ratio of the number of teaching [#permalink]

### Show Tags

04 Jun 2009, 21:11
20
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

61% (00:53) correct 39% (01:05) wrong based on 742 sessions

### HideShow timer Statistics

At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university , what is the maximum number of students possible in a course that has 5 teaching assistants?

A. 130
B. 131
C. 132
D. 133
E. 134
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Mar 2012, 00:35, edited 1 time in total.
Edited the question and added the OA
Manager
Joined: 12 Apr 2006
Posts: 210
Location: India
Re: problem solving question on ratios [#permalink]

### Show Tags

05 Jun 2009, 01:46
2
KUDOS
1
This post was
BOOKMARKED
Not sure whether this is the best possible way but just the way how I solve it.

Teaching Assistants = TA
Students = S

Let assume the ratio of TA/S = $$3/80$$ (Just putting aside the requirement it must be greater)

Let say x be the maximum no of students possible with 5 teaching assistants = $$3/80 = 5/x$$

$$x = 400/3 = 133.33$$. Now for ratio to be greater than $$3/80$$ reduce the denominator. So just rounded it to lowest integer as number of student can't be in decimal. The new ratio is $$5/133$$, which is less than $$3/80$$ thus, 133 is the maximum number of students possible.
Intern
Joined: 25 Sep 2010
Posts: 18
At a certain university, the ratio of the number of teaching [#permalink]

### Show Tags

24 Oct 2010, 17:57
3
KUDOS
10
This post was
BOOKMARKED
At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?
A. 130
B. 131
C. 132
D. 133
E. 134

Last edited by Bunuel on 01 Feb 2012, 14:24, edited 1 time in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 44322
Re: PS question: need help [#permalink]

### Show Tags

24 Oct 2010, 18:10
3
KUDOS
Expert's post
2
This post was
BOOKMARKED
At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?
A. 130
B. 131
C. 132
D. 133
E. 134

Given: $$\frac{assistants}{students}>\frac{3}{80}$$ --> $$assistants=5$$, so $$\frac{5}{s}>\frac{3}{80}$$ --> $$s_{max}=?$$

$$\frac{5}{s}>\frac{3}{80}$$ --> $$s<\frac{5*80}{3}\approx{133.3}$$ --> so $$s_{max}=133$$.

_________________
Intern
Joined: 05 Nov 2010
Posts: 48
Re: problem solving question on ratios [#permalink]

### Show Tags

16 Dec 2010, 14:36
can someone explain in further detail the relationship between the teaching assistants to the number of students in any course must always be greater than 3:80 and how to reason through this portion? I understand how to solve for x. Once I was at this point I think was stumped on which number to select and inevitably chose to round up. My rational being .33 of a student is not possible therefore it must represent the position of an entire student. Thoughts? Help?
Math Expert
Joined: 02 Sep 2009
Posts: 44322
Re: problem solving question on ratios [#permalink]

### Show Tags

16 Dec 2010, 14:47
8
KUDOS
Expert's post
7
This post was
BOOKMARKED
spyguy wrote:
can someone explain in further detail the relationship between the teaching assistants to the number of students in any course must always be greater than 3:80 and how to reason through this portion? I understand how to solve for x. Once I was at this point I think was stumped on which number to select and inevitably chose to round up. My rational being .33 of a student is not possible therefore it must represent the position of an entire student. Thoughts? Help?

At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?
A. 130
B. 131
C. 132
D. 133
E. 134

Given: $$\frac{assistants}{students}>\frac{3}{80}$$ --> $$assistants=5$$, so $$\frac{5}{s}>\frac{3}{80}$$ --> $$s_{max}=?$$

$$\frac{5}{s}>\frac{3}{80}$$ --> $$s<\frac{5*80}{3}\approx{133.3}$$ --> so $$s_{max}=133$$.

$$\frac{assistants}{students}>\frac{3}{80}$$ relationship means that if for example # of assistants is 3 then in order $$\frac{assistants}{students}>\frac{3}{80}$$ to be true then # of students must be less than 80 (so there must be less than 80 students per 3 assistants) on the other hand if # of students is for example 80 then the # of assistants must be more than 3 (so there must be more than 3 assistants per 80 students).

Hope it's clear.
_________________
Intern
Joined: 05 Nov 2010
Posts: 48
Re: problem solving question on ratios [#permalink]

### Show Tags

16 Dec 2010, 14:57
Bunuel,

That is very clear. Thanks for breaking it down like that as it is more clear in order to solve future problems.
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1935

### Show Tags

06 Feb 2011, 11:15
1
KUDOS
A ratio of Teacher/Student > 3/80

In words;
3 Teachers teach < 80 students
1 teacher teaches < 80/3 students
5 teachers teach < (80/3)*5 students
5 teachers teach < 400/3 students
5 teachers teach < 133.33 students

Students can only be integers
5 teachers teach < 134 students

or a maximum of 133 Students.

Ans: "D"
_________________
Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 258
Location: India
Concentration: General Management, Entrepreneurship

### Show Tags

12 Mar 2012, 23:42
1
KUDOS
hi,

I solved it this way, any suggestions always welcome

c/b > 3/80 ( from question)

5/b > 3 / 80
(80 x 5 / 3) > b

This reduces to

133.3333 > b

So the number of burgers have to be less than 133.33 & as u dont get 0.33 burger in Mc Donalds Max burgers is 133

Give me a Big Kudoos Meal Combo if this helps
_________________

Giving +1 kudos is a better way of saying 'Thank You'.

Last edited by boomtangboy on 12 Mar 2012, 23:55, edited 1 time in total.
Manager
Joined: 09 Jul 2013
Posts: 110
Re: At a certain university, the ratio of the number of teaching [#permalink]

### Show Tags

26 Jan 2016, 14:53
4
KUDOS
The question states that the ratio must always be greater than 3:80, not the number of students (or burgers). So when you calculate the ratio $$\frac{5}{x}>\frac{3}{80}$$, increasing the value of $$x$$ will decrease the ratio $$\frac{5}{x}$$, and decreasing the value of $$x$$ will increase the ratio $$\frac{5}{x}$$.

If you calculate the number of burgers to be 133.3, then decide whether to round up or down, understand what will happen to the ratio of $$\frac{5}{x}$$.

If $$\frac{5}{133.33}=\frac{3}{80}$$, and that is the minimum (because $$\frac{5}{x}$$ must always be greater than $$\frac{3}{80}$$), what happens if you round $$x$$ up to 134? Is $$\frac{5}{134}$$ > or < $$\frac{3}{80}$$?

As explained above, if you increase $$x$$ to 134, then the ratio $$\frac{5}{x}$$ is decreased, and it will be less than the minimum of $$\frac{3}{80}$$. If you round $$x$$ down to 133, then the ratio $$\frac{5}{x}$$ will increase, and you will not violate the condition that it must always be greater than $$\frac{3}{80}$$.

Looking at it another way, if we know that the ratio of assistants to students must always be greater than 3:80, then we know that for any given number of assistants, there is a maximum number of students allowed. For every assistant, a maximum of 26.66 students are allowed (80/3). So if there is 1 assistant and 27 students, that is too many. 26 is the maximum number of students allowed if there is only 1 assistant in order to keep the ratio greater than 3:80. Using the same logic, if there are 5 assistants, then the maximum number of students allowed is 133.33. If there were 134 students that would be more than the maximum, therefore the maximum number of students allowed is 133.

Does that help?

Cheers
_________________

Dave de Koos

SVP
Joined: 08 Jul 2010
Posts: 2017
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: At a certain university, the ratio of the number of teaching [#permalink]

### Show Tags

27 Jan 2016, 06:59
scorpio7 wrote:
At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university , what is the maximum number of students possible in a course that has 5 teaching assistants?

A. 130
B. 131
C. 132
D. 133
E. 134

$$\frac{Assistant}{Student} > \frac{3}{80}$$

$$\frac{5}{Student} > \frac{3}{80}$$

$$Student < \frac{(5*80)}{3}$$

$$Student < \frac{(400)}{3}$$

i.e. $$Student < 133.33$$

i.e. Maximum value of No. of students = 133

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 195
Location: India
Concentration: General Management, Marketing
GMAT Date: 11-23-2015
GPA: 3.6
WE: Science (Other)
At a certain university, the ratio of the number of teaching [#permalink]

### Show Tags

25 Feb 2016, 12:56
Brute Force Method:

$$\frac{3}{80}$$ As we are looking to a similar ratio for 5 assistants instead of 3, convert the both numerator (3) and denominator (80) to multiple of 5 by multiplying with 5

$$\frac{3*5}{80*5}$$equivalent to

$$\frac{15}{400}$$

Now as we need ratio for 05 assistants; again divide both numerator and denominator with 3. Pay attention to denominator which we need to answer:

$$\frac{5}{133.33}$$ (Post division of both numerator and denominator with 03)

DONE

Maximum students could be 133 because if students 134 ratio would be less.

Hope it helps!!!!
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2319
Location: United States (CA)
Re: At a certain university, the ratio of the number of teaching [#permalink]

### Show Tags

21 Mar 2017, 06:13
1
KUDOS
Expert's post
satishreddy wrote:
At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?
A. 130
B. 131
C. 132
D. 133
E. 134

We are given that the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80, and we need to determine the maximum number of students possible in a course that has 5 teaching assistants. Let’s use the following formula, in which t = 5 = the number of teaching assistants and s = the number of students.

t/s> 3/80

5/s > 3/80

400 > 3s

400/3 > s

133.33 > s

Since s must be a whole number, the largest possible value of s is 133.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 22 Oct 2017
Posts: 31
Re: At a certain university, the ratio of the number of teaching [#permalink]

### Show Tags

03 Nov 2017, 07:19
Does anybody know how I can solve the Problem with a ratio box?
Re: At a certain university, the ratio of the number of teaching   [#permalink] 03 Nov 2017, 07:19
Display posts from previous: Sort by