Answer questions on the basis of information given in the following case.
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.
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)?
From the given information, we can draw the venn diagram as follows.
The total number of electives = 20
b + 2a + 3x + 1 = 20
b + 2a + 3x = 19
We are given that only G-type electives is 2. Thus, b = 2.
Since a < b, the only possible value of a = 1.
Thus, 2 + 2(1) + 3x = 19
x = 5
Thus, the venn diagram becomes.
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Vijay is interested in J and wants to avoid Q. Thus, he can participate in J and JG subjects.
Raj is interested in G followed by Q. Thus, he can participate in G, Q, and GQ electives.
Since there is no common region between the interests of Vijay and Raj, there is a possibility of them avoiding each other.
Hence, the answer is option A.
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