CAT 2018 Slot 2 — DILR Question 15
Answer the following question based on the information given below.
Fun Sports (FS) provides training in three sports – Gilli-danda (G), Kho-Kho (K), and Ludo (L). Currently it has an enrollment of 39 students each of whom is enrolled in at least one of the three sports. The following details are known:
- The number of students enrolled only in L is double the number of students enrolled in all the three sports.
- There are a total of 17 students enrolled in G.
- The number of students enrolled only in G is one less than the number of students enrolled only in L.
- The number of students enrolled only in K is equal to the number of students who are enrolled in both K and L.
- The maximum student enrollment is in L.
- Ten students enrolled in G are also enrolled in at least one more sport.
Due to academic pressure, students who were enrolled in all three sports were asked to withdraw from one of the three sports. After the withdrawal, the number of students enrolled in G was six less than the number of students enrolled in L, while the number of students enrolled in K went down by one. After the withdrawal, how many students were enrolled in both G and K?
Answer & solution
Answer: 2
Out of 4 students who are enrolled in all the three, suppose ‘a’ students dropped out of L and ‘b’ students dropped out of K. Therefore the number of students who dropped out of G = 4 - a - b.
Therefore we have the following:
If the number of students enrolled in K reduced by 1 that means out of the 4 students who had enrolled in all the three, one student dropped out of K i.e. b = 1.
Now, if the number of students enrolled in G was 6 less than the number of students enrolled in L, we have the following:
(7 + w + a + 6 − w + b) + 6
= 6 − w + b + 9 − a − b + 8
∴19 + a + b = 23 − w − a
∴2a + b + w = 4
Since b = 1, the only solution for the equation 2a + b + w = 4 is a = 1, b = 1 and w = 1.
Now both the questions can be answered.
The required number of students = w + a = 2.
Answer: 2