In a certain math department, students are required to enroll in eithe

Question

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%

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

Kurtosis · Answer

Let number of students enrolled in calculus = x
Number of students enrolled in Trigonometry = 1.5x
Total number of students = x + 1.5x = 2.5x

Number of students enrolled in beginner calculus course = 0.6x
4/5 of Total are in beginner courses --> Number of students in beginner courses = (4/5)*2.5x = 2x
Number of students enrolled in beginner trigonometry courses = 2x - 0.6x = 1.4x

Number of students in advanced calculus courses = x - 0.6x = 0.4x
Number of students in advanced trigonometry courses = 1.5x - 1.4x = 0.1x

Probability that an advanced Trigonometry student is selected = (Number of ways of selecting one student from advanced trigonometry course)/(Number of ways of selecting one student from total)

Assume x = 100

Probability = 10C1/250C1 = 10/250 = 1/25 = 4%

Answer: A

chetan2u · Answer

Hi,
 Vyshak  has told you the exact method ..

However if you get this in exam and are unable to move ahead, you can make intelligent guess..
 since ONLY 1/5 of students are in ADVANCED course, picking a advanced course student itself is 1/2 or 20%.. 
 so our answer has to be less than 20%... 
so A and B are left... 
 This was easy to get probability up from 1/5 to 1/2 of getting the answer correct

The second step requires a bit of visualization 
Now calculus : trig = 2:3..
so 40 % of C added with 16% of T should give a value > 20%, when their ratios are 2:3
SO ans 4%
A
A

LakerFan24 · Answer

Any addtl methods?

Not sure how to compute 10C1 and 250C1

Bunuel · Answer

C stands for combinations. 10C1 = 10!/(1!*(10-1)!) = 10 and 250C1 = 250!/(1!*(250-1)!) = 250.

Combinatorics Made Easy!

Theory on Combinations

DS questions on Combinations 
 PS questions on Combinations

Hope it helps.

Sash143 · Answer

Solve for C. Please see the attachment.

C+1.5C = 100
C = 40.

Substitute C = 40 wherever indicated. In the "advanced" box you'll get 16 + 4 = 20. 
Probability will be 4/100 or 4%.

EMPOWERgmatRichC · Answer

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

GMAT assassins aren't born, they're made,
Rich

zishu912 · Answer

Lets say there are 50 students in calculus, therefore number students in Trigonometry is 75(50% greater than number of students in calculus)

60 % of calculus students enrolled in beginner = 30 so there are 20 who were enrolled in advanced calculus

Total students = 50 + 75 = 125
Out of 125 total number of students enrolled in beginner class is 4/5 * 125 = 100

Out of 100, 30 enrolled for beginner calculus class and rest 70 enrolled for trigonometry beginner class, only 5 joined advanced trigonometry

so the probability that student selected is from advanced trigonometry is 5/125 * 100 = 4 %

fskilnik · Answer

? = \frac{{{	ext{Trig}}\,\, \cap \,\,{	ext{Adv}}}}{{{	ext{Total}}}}

Good mix of the  k technique  with the  grid  (=double matrix, table, you-name-it)!

https://preview.ibb.co/mr5Cip/11-Oct18-8v.gif

?\,\,\, = \,\,\,\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.

ScottTargetTestPrep · Answer

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

robu1 · Answer

bumpbot · Answer

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In a certain math department, students are required to enroll in eithe

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