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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

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

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

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Mon Dec 17, 2018 10:46 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

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)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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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