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Bright Engineering College Electives Selection

XAT 2015 · Decision Making · Hard · Data Interpretation

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Passage / data set

Bright Engineering College (BEC) has listed 20 elective courses for the next term and students have to choose any 7 of them. Simran, a student of BEC, notices that there are three categories of electives: Job - oriented (J), Quantitative - oriented (Q) and Grade - oriented (G). Among these 20 electives, some electives are both Job and Grade - oriented but are not Quantitative - oriented (JG type). QJ type electives are both job and Quantitative - oriented but are not Grade - oriented and QG type electives are both Quantitative and Grade - oriented but are not Job - oriented. Simran also notes that the total number of QJ type electives is 2 less than QG type electives. Similarly, the total number of QG type electives is 2 less than JG type and there is only 1 common elective (JQG) across three categories. Furthermore, the number of only Quantitative - oriented electives is same as only Job - oriented electives, but less than the number of only Grade - oriented electives. Each elective has at least one registration and there is at least one elective in each category, or combinations of categories.

Question 1 of 3

On her way back Simran met her friend Raj and shared the above information. Raj is preparing for XAT and is only interested in Grade - oriented (G) electives. He wanted to know the number of G - type electives being offered. Simran replied, "You have all the information. Calculate the number of G - type electives yourself. It would help your XAT preparation". Raj calculates correctly and says that there can be _______ possible answers. Which of the following options would best fit the blank above?

  1. A.

    3

  2. B.

    5

  3. C.

    8

  4. D.

    9

  5. E.

    11

Answer

B

Explanation

Let the number of only Q and only J electives be aa. Let only G electives be bb with b>ab > a. Let QJ=x−2QJ = x - 2, QG=xQG = x, and JG=x+2JG = x + 2 where x>2x > 2. The total number of electives is 2a+b+3x+1=20  ⟹  2a+b+3x=192a + b + 3x + 1 = 20 \implies 2a + b + 3x = 19. Total G-type electives g=b+2x+3g = b + 2x + 3. Testing integer values of xx:

  • For x=3  ⟹  2a+b=10x = 3 \implies 2a + b = 10. (a,b)∈{(1,8),(2,6),(3,4)}  ⟹  g∈{17,15,13}(a,b) \in \{(1,8), (2,6), (3,4)\} \implies g \in \{17, 15, 13\}.
  • For x=4  ⟹  2a+b=7x = 4 \implies 2a + b = 7. (a,b)∈{(1,5),(2,3)}  ⟹  g∈{16,14}(a,b) \in \{(1,5), (2,3)\} \implies g \in \{16, 14\}.
  • For x=5  ⟹  2a+b=4x = 5 \implies 2a + b = 4. (a,b)=(1,2)  ⟹  g=13(a,b) = (1,2) \implies g = 13. Thus, gg can take values 13,14,15,16,1713, 14, 15, 16, 17, giving 5 possible answers. Hence, option B is correct.

Question 2 of 3

Simran prefers J - type electives and wants to avoid Q - type electives. She noted that the number of only J - type electives is 3. Raj's preference is G - type electives followed by Q - type electives. However, they want to take as many common electives as possible. What is the maximum number of electives that can be common between them, without compromising their preferences?

  1. A.

    3

  2. B.

    4

  3. C.

    5

  4. D.

    7

  5. E.

    Not possible to answer from the above information.

Answer

C

Explanation

Given a=3a = 3, 2a+b+3x=19  ⟹  b+3x=132a + b + 3x = 19 \implies b + 3x = 13. To maximize xx with b>a=3b > a = 3, we choose b=4b = 4 and x=3x = 3. The electives common to both without violating preferences are the JGJG electives and JQGJQG electives, totaling x+2=3+2=5x + 2 = 3 + 2 = 5. Hence, option C is correct.

Question 3 of 3

Vijay and Raj want to avoid each other. Vijay is interested in J - type electives and wants to avoid Q - type electives. Raj's preference is G - type electives followed by Q - type electives. Raj noted that the number of only G - type electives is 2. Is there a possibility that they would not share any common electives(s)?

  1. A.

    Yes. There is a possibility

  2. B.

    No. They would meet in one elective.

  3. C.

    No. They would not be able to avoid in two electives.

  4. D.

    No. They meet in five electives.

  5. E.

    Cannot be solved with the information given.

Answer

A

Explanation

Vijay can select electives strictly from J and JG categories, whereas Raj can choose electives from G, Q, and GQ categories. Since there is no forced overlap between these respective elective sets, it is possible for them to avoid each other completely. Hence, option A is correct.

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