Jun 16 07:00 AM PDT  09:00 AM PDT Get personalized insights and an accurate assessment of your current quant score to achieve your Target Quant Score. Jun 16 09:00 PM PDT  10:00 PM PDT For a score of 4951 (from current actual score of 40+). AllInOne Standard & 700+ Level Questions (150 questions) Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 28 Jun 2008
Posts: 38

At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
Updated on: 13 Mar 2012, 00:35
Question Stats:
62% (01:35) correct 38% (01:55) wrong based on 605 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, 21:11.
Last edited by Bunuel on 13 Mar 2012, 00:35, edited 1 time in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 55609

Re: problem solving question on ratios
[#permalink]
Show Tags
16 Dec 2010, 14:47
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.
_________________




Intern
Joined: 25 Sep 2010
Posts: 15

At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
Updated on: 01 Feb 2012, 14:24
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, 17:57.
Last edited by Bunuel on 01 Feb 2012, 14:24, edited 1 time in total.
Edited the question




Manager
Joined: 12 Apr 2006
Posts: 191
Location: India

Re: problem solving question on ratios
[#permalink]
Show Tags
05 Jun 2009, 01:46
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: 55609

Re: PS question: need help
[#permalink]
Show Tags
24 Oct 2010, 18:10
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.
_________________



Intern
Joined: 05 Nov 2010
Posts: 40

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?



Intern
Joined: 05 Nov 2010
Posts: 40

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.



Retired Moderator
Joined: 20 Dec 2010
Posts: 1749

Re: problem solving
[#permalink]
Show Tags
06 Feb 2011, 11:15
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"
_________________



Manager
Status: May The Force Be With Me (DDAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 198
Location: India
Concentration: General Management, Entrepreneurship

Re: Chefs to burgers
[#permalink]
Show Tags
Updated on: 12 Mar 2012, 23:55
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, 23:42.
Last edited by boomtangboy on 12 Mar 2012, 23:55, 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, 14:53
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: 2940
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 Answer: option D
_________________
Prosper!!!GMATinsightBhoopendra 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 Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 181
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, 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: 6521
Location: United States (CA)

Re: At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
21 Mar 2017, 06:13
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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



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?



Intern
Joined: 02 Jan 2017
Posts: 45

At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
27 Jan 2019, 16:03
Hello Bunuel, As per your explanation here, then max should be A: 130 to be greater than 3/80. Is my thinking correct. Bunuel wrote: 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.



Manager
Joined: 09 Jul 2013
Posts: 109

Re: At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
28 Jan 2019, 09:24
Hi Aaron, Bunuel's explanation is, of course, correct. The answer is D. Think of it this way: If you have a ratio \(\frac{a}{b}\), and you want to increase the value of that ratio, there are two ways you can do that. You can either increase the numerator or decrease the denominator. In our case, we want to choose the denominator so that the resulting ratio is less than the given value \(\frac{3}{80}\). To do that we will have to increase the denominator as much as we can so that the ratio \(\frac{assistants}{students}\) is still greater than \(\frac{3}{80}\). But if we increase the denominator too much the ratio of assistants to students will drop below our limit of \(\frac{3}{80}\). Imagine a simpler scenario where the target ratio wasn't \(\frac{3}{80}\), but instead \(\frac{5}{80}\). In that case the greatest number of students that would be allowed and still maintain the ratio of assistants to students greater than \(\frac{5}{80}\) would be 79. One more student and the ratio would be equal to, not greater than \(\frac{5}{80}\). In our problem, we want the maximum number of students such that the ratio \(\frac{assistants}{students}>\frac{3}{80}\). You can solve this algebraically, as has been done above to find that students must be less than 133.3. The largest integer less than 133.3 is 133. If we decrease the students down to 130, then the ratio will indeed be larger than the target of \(\frac{3}{80}\), but we still have space to add more students and still maintain the ratio greater than \(\frac{3}{80}\). I hope it helps! aaronTgmaT wrote: Hello Bunuel, As per your explanation here, then max should be A: 130 to be greater than 3/80. Is my thinking correct. Bunuel wrote: 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.
_________________
Dave de Koos GMAT aficionado



Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 304

At a certain university, the ratio of the number of teaching
[#permalink]
Show Tags
10 Jun 2019, 09:14
Another way to do it using remainders:
80 students /3 professors = 26 Remainder 2/3, so each professor teaches 26 and 2/3 students. (26 Remainder 2/3) * 5 = 130 + 10/3 or 133 and 1/3 Because students have to be an integer, the max number that can be taught is D) 133




At a certain university, the ratio of the number of teaching
[#permalink]
10 Jun 2019, 09:14






