CAT 2018 Set-2 | Question: 51

Question

Fun Sports $\text{(FS)}$ provides training in three sports-Gilli-danda $\text{(G)}$, Kho-Kho $\text{(K)}$, and Ludo $\text{(L)}$. 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:

1. The number of students enrolled only in $\text{L}$ is double the number of students enrolled in all the three sports.
2. There are a total of $17$ students enrolled in $\text{G}$.
3. The number of students enrolled only in $\text{G}$ is one less than the number of students enrolled only in $\text{L}$.
4. The number of students enrolled only in $\text{K}$ is cqual to the number of students who are enrolled in both $\text{K}$ and $\text{L}$
5. The maximum student enrollment is in $\text{L}$.
6. Ten students enrolled in $\text{G}$ are also enrolled in at least one more sport.

What is the minimum number of students enrolled in both $\text{G}$ and $\text{L}$ but not in $\text{K}?$