November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 28 Jun 2008
Posts: 39

At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
Updated on: 12 Mar 2012, 23:35
Question Stats:
64% (00:56) correct 36% (01:04) wrong based on 781 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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by scorpio7 on 04 Jun 2009, 20:11.
Last edited by Bunuel on 12 Mar 2012, 23:35, edited 1 time in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 50578

Re: problem solving question on ratios
[#permalink]
Show Tags
16 Dec 2010, 13:47
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 \(s_{max}=133\). Answer: D. \(\frac{assistants}{students}>\frac{3}{80}\) 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 25 Sep 2010
Posts: 16

At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
Updated on: 01 Feb 2012, 13:24
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
Originally posted by satishreddy on 24 Oct 2010, 16:57.
Last edited by Bunuel on 01 Feb 2012, 13:24, edited 1 time in total.
Edited the question




Manager
Joined: 12 Apr 2006
Posts: 200
Location: India

Re: problem solving question on ratios
[#permalink]
Show Tags
05 Jun 2009, 00:46
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.



Math Expert
Joined: 02 Sep 2009
Posts: 50578

Re: PS question: need help
[#permalink]
Show Tags
24 Oct 2010, 17:10



Intern
Joined: 05 Nov 2010
Posts: 43

Re: problem solving question on ratios
[#permalink]
Show Tags
16 Dec 2010, 13:36
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?



Intern
Joined: 05 Nov 2010
Posts: 43

Re: problem solving question on ratios
[#permalink]
Show Tags
16 Dec 2010, 13:57
Bunuel,
That is very clear. Thanks for breaking it down like that as it is more clear in order to solve future problems.



Retired Moderator
Joined: 20 Dec 2010
Posts: 1829

Re: problem solving
[#permalink]
Show Tags
06 Feb 2011, 10:15
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"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Status: May The Force Be With Me (DDAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 221
Location: India
Concentration: General Management, Entrepreneurship

Re: Chefs to burgers
[#permalink]
Show Tags
Updated on: 12 Mar 2012, 22:55
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'.
Originally posted by boomtangboy on 12 Mar 2012, 22:42.
Last edited by boomtangboy on 12 Mar 2012, 22:55, edited 1 time in total.



Manager
Joined: 09 Jul 2013
Posts: 109

Re: At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
26 Jan 2016, 13:53
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 GMAT aficionado



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2698
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, 05:59
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 Answer: option D
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 184
Location: India
Concentration: General Management, Marketing
GMAT Date: 11232015
GPA: 3.6
WE: Science (Other)

At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
25 Feb 2016, 11:56
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: 4171
Location: United States (CA)

Re: At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
21 Mar 2017, 05:13
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. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy 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, 06:19
Does anybody know how I can solve the Problem with a ratio box?



NonHuman User
Joined: 09 Sep 2013
Posts: 8766

Re: At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
11 Nov 2018, 02:27
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: At a certain university, the ratio of the number of teaching &nbs
[#permalink]
11 Nov 2018, 02:27






