CAT 2018 Question Paper | CAT LR DI

CAT Questions

This puzzle set is a beautiful depiction of the value of the products of three companies in a 'picto-graphical' format. This set might seem a bit confusing at the first glance, however, the graph clearly explains the puzzle's intention. Furthermore, the puzzle also presents a set of conditions that is instrumental in cracking the data. So, try your hands on this beautiful set from the CAT previous year paper and see your CAT Online Preparation go onward and upwards!

CAT DILR : CAT 2018 Question Paper Slot 2

Set 3 : Fun Sports Club

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

Question 1 : What is the minimum number of students enrolled in both G and L but not in K? [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question on CAT DILR

From condition 3, we get the above diagram.

Condition 6 tells us p – 1 = 7. G-total = 17. G and something else = 10. G-only should be 7.

From condition 1, we get the above diagram.

From condition 6, we can get the diagram.

From condition 4, we get the above diagram.

Now we know that the total = 39.

From condition 5,
Number of students in L = 4 + 5 + 8 + 6 – x = 23- x.
Number of students in K = 4 + 5 + 9 + x = 18 + x.
We know that 23 – x > 18 + x.
5 > 2x. x < \\frac{5}{2}).
x could be 0, 1 or 2.

For 6 - x to be minimum, x should be maximum i.e. x should take 2.
Therefore the minimum number of students enrolled in both G and L but not in K is 4.

The question is "What is the minimum number of students enrolled in both G and L but not in K? [TITA]"

Hence, the answer is 4

 

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