Fun Sports Club

CAT 2018 Slot 2 · DILR · Hard · Logical Reasoning

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Passage / data set

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 of 4

What is the minimum number of students enrolled in both G and L but not in K?

Answer

4

Explanation

Let the 7 regions of the 3-set Venn diagram be:

  • Only G = gg, Only K = kk, Only L = ll
  • G and K only = aa, G and L only = bb, K and L only = cc
  • All three = dd

From given facts:

  1. l=2dl = 2d
  2. Total G = g+a+b+d=17g + a + b + d = 17
  3. g=l−1=2d−1g = l - 1 = 2d - 1
  4. k=c+dk = c + d
  5. a+b+d=10  ⟹  g=17−10=7a + b + d = 10 \implies g = 17 - 10 = 7. Since g=7g = 7, 2d−1=7  ⟹  2d=8  ⟹  d=42d - 1 = 7 \implies 2d = 8 \implies d = 4. Then l=8l = 8. Since a+b+d=10a + b + d = 10 and d=4d = 4, a+b=6a + b = 6. To minimize bb (both G and L but not K), aa must be maximized. Since a≤2a \le 2, the minimum value for bb is 44.

Question 2 of 4

If the numbers of students enrolled in K and L are in the ratio 19:22, then what is the number of students enrolled in L?

  1. A.

    19

  2. B.

    18

  3. C.

    22

  4. D.

    17

Answer

C

Explanation

From the set calculations, total in L is l+b+c+d=8+b+c+4=12+b+cl + b + c + d = 8 + b + c + 4 = 12 + b + c. Given ratio K:L=19:22K : L = 19 : 22, L must be a multiple of 22 or equal to 22. Checking valid values consistent with total enrollment of 39 gives L=22L = 22.

Question 3 of 4

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

2

Explanation

Since d=4d = 4 students were enrolled in all three, each withdrew from one sport. Since enrollment in K went down by 1, 1 student left K (so withdrew from K and remained in G and L). The remaining 3 students in all three withdrew from either G or L. Calculating the remaining region overlaps gives the number of students enrolled in both G and K after withdrawal as 2.

Question 4 of 4

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 L?

  1. A.

    5

  2. B.

    8

  3. C.

    7

  4. D.

    6

Answer

C

Explanation

Following the withdrawal breakdown from Q3, the number of students enrolled in both G and L after redistribution becomes 7.

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