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

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In a certain math department, students are required to enroll in eithe  [#permalink]

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02 Apr 2016, 03:54
11
00:00

Difficulty:

45% (medium)

Question Stats:

78% (02:56) correct 22% (02:51) wrong based on 250 sessions

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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%

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In a certain math department, students are required to enroll in eithe  [#permalink]

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02 Apr 2016, 04:16
2
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%

Attachments

IMG_20160402_163946.jpg [ 1.6 MiB | Viewed 2785 times ]

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Re: In a certain math department, students are required to enroll in eithe  [#permalink]

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02 Apr 2016, 05:16
1
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%

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
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Re: In a certain math department, students are required to enroll in eithe  [#permalink]

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22 Jan 2017, 17:19

Not sure how to compute 10C1 and 250C1
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Posts: 55623
Re: In a certain math department, students are required to enroll in eithe  [#permalink]

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23 Jan 2017, 01:47
LakerFan24 wrote:

Not sure how to compute 10C1 and 250C1

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

Theory on Combinations

DS questions on Combinations
PS questions on Combinations

Hope it helps.
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Re: In a certain math department, students are required to enroll in eithe  [#permalink]

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27 Feb 2017, 02:00
1
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%

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%.
Attachments

Cal&Tri.png [ 13.77 KiB | Viewed 2092 times ]

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Re: In a certain math department, students are required to enroll in eithe  [#permalink]

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27 Feb 2017, 22:04
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%

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Re: In a certain math department, students are required to enroll in eithe  [#permalink]

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16 May 2018, 11:20
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%

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 %
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In a certain math department, students are required to enroll in eithe  [#permalink]

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11 Oct 2018, 12:23
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%

$$? = \frac{{{\text{Trig}}\,\, \cap \,\,{\text{Adv}}}}{{{\text{Total}}}}$$

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

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

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

Regards,
Fabio.
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Re: In a certain math department, students are required to enroll in eithe  [#permalink]

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18 Oct 2018, 18:22
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%.

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Re: In a certain math department, students are required to enroll in eithe   [#permalink] 18 Oct 2018, 18:22
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