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

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by BTGmoderatorDC » Mon Dec 17, 2018 10:46 pm

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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

OA D

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by Brent@GMATPrepNow » Tue Dec 18, 2018 7:01 am
BTGmoderatorDC 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 can solve this using equivalent ratios
We're comparing teaching assistants/number of students

Let x = number of students possible
We can write: 5/x = 3/80
Cross multiply to get: 3x = (5)(80)
Simplify: 3x = 400
Solve: x = 400/3 = 133 1/3 = 133.3333

Since 134 students would exceed to 3:80 ratio, the maximum number of students possible in a course that has 5 teaching assistants is 133

Answer: D

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by fskilnik@GMATH » Wed Dec 19, 2018 5:41 am
BTGmoderatorDC 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
Source: GMAT Prep
$$t\,\,({\rm{ta}})\,\,,\,\,s\,\,\left( {{\rm{student}}} \right)\,\,\,\, \ge \,\,1\,\,\,{\rm{ints}}\,\,\,\,\,\,\left( * \right)$$
$${t \over s} > {3 \over {80}}\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,{s_{\,\max }}\,\,\,{\rm{when}}\left( {{\rm{for}}} \right)\,\,\,t = 5$$

$$\frac{5}{s} > \frac{3}{{80}}\,\,\,\,\mathop \Leftrightarrow \limits^{80\,s\,\, > \,\,0} \,\,\,80 \cdot 5 > 3s\,\,\,\,\, \Leftrightarrow \,\,\,\,\,s < 5\left( {\frac{{78 + 2}}{3}} \right) = \underleftrightarrow {5\left( {26 + \frac{2}{3}} \right) = \,130 + \frac{{10}}{3}} = 133\frac{1}{3}\,$$
$$s < 133{1 \over 3}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,? = 133\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Scott@TargetTestPrep » Sun Mar 03, 2019 6:29 pm
BTGmoderatorDC 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

OA D

Source: GMAT Prep
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 set up a proportion, 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

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