Question

In a small college, students are allowed to take only one specialization. Traditionally, only two specializations are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects. Students enrolled in Science are not allowed to take either Economics or Political Science, while students enrolled in Arts are not allowed to take either Physics or Mathematics.
Recently, the college has started a third specialization called MatEco that requires students to take Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or Political Science. When the college opens this new specialization for enrolment, it allows students, originally enrolled in Science or Arts, to switch to MatEco.
From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number of Science students twice the number of Arts students. After this, from among the students who originally enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the number of Science students.
In total, how many students, from among those originally enrolled in Science or Arts, are now taking Economics?

• A. 45
• B. 65
• C. 80
• D. 95
• E. None of the remaining options is correct.

Answer 1

The Correct Option is D

Let the initial count of Science students be S and Arts students be A.

Condition 1 Analysis: After 20 students transfer from Arts to MatEco, the Arts student count becomes A − 20. The Science student count is then double the remaining Arts students, resulting in 2(A − 20).

S = 2(A − 20)

S = 2A − 40

Condition 2 Analysis: When 45 Science students move to MatEco, the remaining Science students are S − 45. The Arts student count is then twice the remaining Science students.

A − 20 = 2(S − 45)

Substitute S = 2A − 40 into the equation:

A − 20 = 2((2A − 40) − 45)

Simplify:

A − 20 = 2(2A − 85)

A − 20 = 4A − 170

3A = 150 > A = 50

Calculate S:

S = 2A − 40 = 2(50) − 40 = 60

Calculate the total number of students. The total comprises: - The 20 students who moved from Arts to MatEco. - The remaining A − 20 Arts students. - The 45 Science students who moved to MatEco.

Total: (A − 20) + 20 + 45 = A + 45 = 50 + 45 = 95

Answer: 95