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In a certain math department, students are required to

by AAPL » Thu Oct 11, 2018 7:01 am

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In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 60% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?

A. 4%
B. 16%
C. 20%
D. 24%
E. 40%

OA A.
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by fskilnik@GMATH » Thu Oct 11, 2018 11:16 am
AAPL wrote:Veritas Prep

In a certain math department, students are required to enroll in either Calculus or Trigonometry BUT NOT BOTH, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 60% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?

A. 4%
B. 16%
C. 20%
D. 24%
E. 40%
$$? = {{{\rm{Trig}}\,\, \cap \,\,{\rm{Adv}}} \over {{\rm{Total}}}}$$
Good mix of the k technique with the grid (=double matrix, table, you-name-it)!

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$$?\,\,\, = \,\,\,\frac{k}{{25k}}\,\,\, = \,\,\,\frac{{1 \cdot \boxed4}}{{25 \cdot \boxed4}}\,\,\, = \,\,\,4\% $$

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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by Scott@TargetTestPrep » Thu Oct 18, 2018 5:17 pm
AAPL wrote:Veritas Prep

In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 60% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?

A. 4%
B. 16%
C. 20%
D. 24%
E. 40%
We can assume 60 students are enrolled in Trigonometry and thus 60/1.5 = 40 students are enrolled in Calculus. Furthermore, 0.6 x 40 = 24 students are enrolled in beginner Calculus and hence 16 students are enrolled in advanced Calculus.

Since there are a total of 60 + 40 = 100 students, 4/5 x 100 = 80 students are in the beginner courses. Since 24 students are enrolled in beginner Calculus, 80 - 24 = 56 students are enrolled in beginner Trigonometry. That means 60 - 56 = 4 students are enrolled in advanced Trigonometry. So the probability of selecting such a student at random is 4/100 = 4%.

Answer: A

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by [email protected] » Thu Oct 18, 2018 6:54 pm
Hi All,

This question can be solved by TESTing VALUES and taking the proper notes. We're told that there are two classes (Calculus and Trigonometry) and each is offered in beginner and advanced courses - and that each student is enrolled in just one course.

The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus....

IF.... there are 100 total students
Trigonometry = 60 students
Calculus = 40 students

....and 60% of Calculus students are enrolled in the beginner course....

Calculus = 40 total students
-Beginner = 60% of 40 = 24 students
-Advanced = 40 - 24 = 16 students

... and 4/5 of students are in the beginner courses....

4/5 of 100 = 80 students in beginner courses
-Beginning Calculus = 24 students
-Beginning Trigonometry = 80 - 24 = 56 students

Since there are 60 total Trigonometry students, and 56 of them are in the beginner course, 60 - 56 = 4 students in the advanced Trigonometry course

We're asked for the probability that an advanced Trigonometry student is selected? That would be 4/100 = 4%

Final Answer: A

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Rich
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