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Set Theory - Course Registrations

XAT 2018 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

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In the final semester, an engineering college offers three elective courses and one mandatory course. A student has to register for exactly three courses: two electives and the mandatory course. The registration in three of the four courses is: 45, 55 and 70. What will be the number of students in the elective with the lowest registration?

  1. A.

    35

  2. B.

    40

  3. C.

    42

  4. D.

    45

  5. E.

    Either B or D

Answer

E

Explanation

Let mandatory course be MM and electives be E1,E2,E3E_1, E_2, E_3. Case 1: 70 is mandatory course registration. Total students N=70N = 70. Sum of electives = 2N=1402N = 140. Given elective registrations 45, 55, xx. 45+55+x=140  ⟹  x=4045 + 55 + x = 140 \implies x = 40. Elective counts are 40, 45, 55. Lowest = 40. Case 2: 70 is an elective. Total registrations given = 45, 55, 70 for electives. Total students N=45+55+702=85N = \frac{45 + 55 + 70}{2} = 85. Lowest elective = 45. Hence, lowest elective registration is either 40 or 45.

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