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
At a certain university, the ratio of the number of teaching
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We can solve this using equivalent ratiosBTGmoderatorDC 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'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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Brent
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$$t\,\,({\rm{ta}})\,\,,\,\,s\,\,\left( {{\rm{student}}} \right)\,\,\,\, \ge \,\,1\,\,\,{\rm{ints}}\,\,\,\,\,\,\left( * \right)$$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
$${t \over s} > {3 \over {80}}\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,{s_{\,\max }}\,\,\,{\rm{when}}\left( {{\rm{for}}} \right)\,\,\,t = 5$$
$$\frac{5}{s} > \frac{3}{{80}}\,\,\,\,\mathop \Leftrightarrow \limits^{80\,s\,\, > \,\,0} \,\,\,80 \cdot 5 > 3s\,\,\,\,\, \Leftrightarrow \,\,\,\,\,s < 5\left( {\frac{{78 + 2}}{3}} \right) = \underleftrightarrow {5\left( {26 + \frac{2}{3}} \right) = \,130 + \frac{{10}}{3}} = 133\frac{1}{3}\,$$
$$s < 133{1 \over 3}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,? = 133\,$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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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.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
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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