Question: 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?
Explanation:
Let QJ type electives, only Grade-oriented electives and only Quantitative-oriented electives be z , y and x respectively.
Note: y > x
∴ Number of QG type electives = z + 2
∴ Number of JG type electives = z + 4
The given data can be represented in the form of the following Venn diagram,
Thus, the following equation is obtained,
3z + 2x + y = 13
(x, z ≥ 1 and y ≥ 2 )
For z = 1, 2x + y = 10 and possible values of (x, y): (1, 8), (2, 6) and (3, 4).
For z = 2, 2x + y = 7 and possible values of (x, y): (1, 5) and (2, 3).
For z = 3, 2x + y = 4 and possible values of (x, y): (1, 2).
Now, G = 2z + y + 7
If z = 1, G = 17, 15, 13
If z = 2, G = 16, 14
If z = 3, G = 15
Only 5 unique values of G are possible i.e. 13, 14, 15, 16 and 17.
Hence, option (b).