MBApyq

College Specializations and Economics Students

XAT 2024 · Quantitative Ability & Data Interpretation · Medium · Arithmetic

All XAT 2024 questionsMore Arithmetic questionsAll XAT QADI

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?

  1. A.

    45

  2. B.

    65

  3. C.

    80

  4. D.

    95

  5. E.

    None of the remaining options is correct.

Answer

D

Explanation

Let xx be the initial number of Arts students and yy be the initial number of Science students.

After 20 students switch from Arts to MatEco:

  • Remaining Arts students = x−20x - 20
  • Science students = yy Given: y=2(x−20)  ⟹  2x−y=40y = 2(x - 20) \implies 2x - y = 40 ... (1)

Next, 45 students switch from Science to MatEco:

  • Remaining Science students = y−45y - 45
  • Arts students = x−20x - 20 Given: x−20=2(y−45)  ⟹  x−2y=−70x - 20 = 2(y - 45) \implies x - 2y = -70 ... (2)

Solving (1) and (2): Multiply (1) by 2: 4x−2y=804x - 2y = 80 Subtract (2): 3x=150  ⟹  x=503x = 150 \implies x = 50. From (1), y=2(50)−40=60y = 2(50) - 40 = 60.

Students studying Economics now include:

  • MatEco students: 20+45=6520 + 45 = 65
  • Remaining Arts students: 50−20=3050 - 20 = 30 Total taking Economics = 65+30=9565 + 30 = 95.

Related Arithmetic questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace