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

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At a certain university, the ratio of the number of teaching [#permalink]

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24 Oct 2010, 16:57
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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 01 Feb 2012, 13:24, edited 1 time in total.
Edited the question

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Re: PS question: need help [#permalink]

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24 Oct 2010, 17:10
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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 $$s_{max}=133$$.

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Re: PS question: need help [#permalink]

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25 Oct 2010, 05:03
Bunuel 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

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 $$s_{max}=133$$.

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26 Oct 2010, 09:41
for 80 students, more than 3 teaching assistants are there
so for 5 teaching assistants .... no.of students max is ??

3 ---- 80
5-----?

80*5/3 = 133

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06 Feb 2011, 09:57
t/s > 3/80
s < (80/3) * t
s < 80 * 5/3
s = 133
D

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06 Feb 2011, 10:15
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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"
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Re: At a certain university, the ratio of the number of teaching [#permalink]

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11 Jan 2017, 10:41
Hi, Can someone pleas explain me what exactly does this line mean?

''the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80.''

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Re: At a certain university, the ratio of the number of teaching [#permalink]

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11 Jan 2017, 20:52
deeksha6 wrote:
Hi, Can someone pleas explain me what exactly does this line mean?

''the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80.''

This is explained in the solutions above. It means $$\frac{assistants}{students}>\frac{3}{80}$$
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Re: At a certain university, the ratio of the number of teaching [#permalink]

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11 Jan 2017, 21:54
Thank you for replying Bunuel. See, I understand the algebraic representation of the statement. My problem is

teachers/students > 3/80 means that for every 80 students, there are 3 teachers. therefore, for every 1 teacher, the maximum number of student can be 26.7 rounded off to 26 (cant take 27 coz then the condition wont sustain).Now, if for 1 teacher the max is 26, therefore for 5 teachers the max should be 130, no? Where am I going wrong ??

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Re: At a certain university, the ratio of the number of teaching [#permalink]

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15 Mar 2017, 01:55
I got 133 as answer. But if you compare the ratios.
\frac{3}{80}=0.0375
1)\frac{5}{130}=0.0384
2)Will be less than 2nd option
3)Will be less than 2nd option
4)Will be less than 2nd option
5)Will be less than 2nd option
Since we were told that ratio should be greater than \frac{3}{80} and only option 1 satisfies that. Not sure where i am wrong.
Can someone help me understand this?

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Re: At a certain university, the ratio of the number of teaching [#permalink]

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15 Mar 2017, 02:04
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

let teaching assistant be t and s be the students then
t/s > 3/80
given t=5
5/s>3/80
(400)/3 > s
133.33>s
so s =133

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Re: At a certain university, the ratio of the number of teaching [#permalink]

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21 Mar 2017, 05:13
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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.

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Re: At a certain university, the ratio of the number of teaching [#permalink]

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03 Nov 2017, 06:19
Does anybody know how I can solve the Problem with a ratio box?

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Re: At a certain university, the ratio of the number of teaching   [#permalink] 03 Nov 2017, 06:19
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