CAT DILR Questions | CAT Logical Reasoning questions
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Comprehension
Directions for questions: Read the given instructions carefully and answer the questions accordingly.
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.
CAT/2018.2
Question . 114
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?
Explanatory Answer
Method of solving this CAT DILR Question from Logical Reasoning question
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 < 5/2">5/2.
x could be 0, 1 or 2.
We know that G ∩ K ∩ L = 0. We know that the 4 that were originally here are distributed among the three regions currently having x, 6 – x and 5.
We know that one student leaves K. So, this student should have gone to the region (G and L but not K).
Or, (G and L but not K) will now read 7 – x.
The other three should have opted out of one or the other of G and L. Let us assume m students left G, 3 – m should have left L.
Let us rejig the diagram.
Total number of students in G = 17 – m.
Total number of students in L = 20 + m – x.
20 + m – x – (17 – m) = 3 + 2m – x = 6.
2m – x = 3. x can only take values 0, 1 and 2. 2m = 3 + x.
Or, x has to be 1. m has to be 2.
Both G and K = 3 + x – m. 3 + 1 -2 = 2.
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