CAT 2018 Slot 2 DILR · Set 8 of 8Data InterpretationModerate DifficultyQ29–Q32 · 2 MCQ + 2 TITA

CAT 2018 Slot 2 DILR Set 8: Venn Diagrams (4 Questions) with Solutions

The Venn Diagrams set from the official CAT 2018 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2018 Slot 2 DILR · Questions 29–32

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.

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q29. Venn Diagrams

TITA · +3 / 0

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

Correct Answer

Step-by-step solution

📌 Core Concept

Split the 39 students into the seven regions of a three-set Venn diagram, solve the regions from the clues, then use "maximum enrollment is in L" to bound the GL-only region.

🔢 Step-by-Step Solution

Let

x

be the number in all three sports. Clue 1 gives only-L

=2x

. Let

a

b

c

be the numbers in only GK, only GL and only KL.

Clue 6 says 10 students of G are in at least one more sport, so

a+b+x=10

. Clue 2 gives only-G

=17-10=7

Clue 3 says only-G is one less than only-L, so only-L

=8

. Then

x=4

and

a+b=6

Clue 4 says only-K equals the number in both K and L, which is

c+x=c+4

The total is 39:

7+(c+4)+8+(a+b)+c+4=39

. With

a+b=6

this gives

2c=10

, so

c=5

and only-K

=9

Totals:

G=17

K=9+a+5+4=18+a

L=8+b+5+4=17+b

Clue 5 says L is the largest, so

L\ge K

. Using

a=6-b

17+b\ge 24-b

, which gives

b\ge 3.5

. So

b\ge 4

For

b=4

a=2

K=20

L=21

. L is the maximum, and

L\ge G

also holds.

Quick Check

With

b=4

7+9+8+2+4+5+4=39

, and

L=21>K=20>G=17

Correct Answer: 4

Q30. Venn Diagrams

MCQ · +3 / −1

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?

A) 18
B) 19
C) 17
D) 22

Correct Answer

D) 22

Step-by-step solution

📌 Core Concept

Solve the Venn regions from the clues, express the K and L totals in terms of the unknown split of

a+b=6

, then apply the ratio.

🔢 Step-by-Step Solution

Let

a

b

c

be the numbers in only GK, only GL and only KL, and

x

the number in all three. Clue 6 gives

a+b+x=10

, and clue 2 gives only-G

=7

Clue 3 makes only-L

=8

. Clue 1 then gives

x=4

, so

a+b=6

Clue 4 makes only-K

=c+x=c+4

. The total of 39 gives

7+(c+4)+8+6+c+4=39

, so

c=5

and only-K

=9

Then

K=9+a+5+4=18+a

and

L=8+b+5+4=17+b

Adding:

K+L=35+(a+b)=41

The ratio is

19:22

, and

19+22=41

exactly. So

K=19

and

L=22

This is consistent:

a=1

b=5

, and

L=22

is the maximum enrollment.

Why Not the Others

A (18), B (19) and C (17) are all less than

K+L=41

split in the ratio 19:22. Only 22 fits, and 19 is the K figure.

Correct Answer: D

Q31. Venn Diagrams

TITA · +3 / 0

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?

Correct Answer

Step-by-step solution

📌 Core Concept

Fill the seven Venn regions from the clues, then track where the 4 students enrolled in all three sports go when each drops one sport.

🔢 Step-by-Step Solution

Let

x

be the number enrolled in all three sports, and

d

e

f

the numbers in G and K only, G and L only, and K and L only.

Clue 6: the G students in at least one more sport number

d+e+x=10

. Clue 2 then gives only-G

=17-10=7

Clue 3: only-L

=7+1=8

. Clue 1:

8=2x

, so

x=4

and

d+e=6

Clue 4 compares only-K with everyone enrolled in both K and L, which includes the 4 students in all three: only-K

=f+4

Total:

7+(f+4)+8+6+f+4=39

, so

f=5

and only-K

=9

Totals:

G=17

K=9+d+5+4=18+d

L=8+e+5+4=17+e

. Clue 5 (L is the largest) with

d=6-e

gives

17+e>24-e

, so

e\ge 4

and

d\le 2

The 4 triple-sport students each drop one sport:

p

leave G,

q

leave L and exactly 1 leaves K (K fell by one), so

p+q=3

After:

G=17-p

and

L=17+e-q

. The condition

G=L-6

gives

q-p=e-6

. With

p+q=3

q=\dfrac{e-3}{2}

Only

e=5

(from 4, 5, 6) makes

q

a whole number. So

e=5

d=1

q=1

and

p=2

After the withdrawal nobody is in all three sports. The students in both G and K are the

d=1

who were in G and K only, plus the

q=1

triple-sport student who dropped L and kept G and K:

1+1=2

Reading of Clue 4

"Enrolled in both K and L" counts everyone in both sports, including the triple-sport students. Reading it as "K and L only" leaves two possible arrangements (an answer of 3 or 4) and contradicts the other answers in this set, so the inclusive reading is the intended one.

Quick Check

Before:

7+9+8+1+5+5+4=39

, with

L=22>K=19>G=17

. After:

G=15

L=21

and

15=21-6

; K went from 19 to 18.

Correct Answer: 2

Q32. Venn Diagrams

MCQ · +3 / −1

A) 7
B) 6
C) 5
D) 8

Correct Answer

B) 6

Step-by-step solution

📌 Core Concept

Fill the seven Venn regions from the clues, then track where the 4 students enrolled in all three sports go when each drops one sport.

🔢 Step-by-Step Solution

Let

x

be the number enrolled in all three sports, and

d

e

f

the numbers in G and K only, G and L only, and K and L only.

Clue 6: the G students in at least one more sport number

d+e+x=10

. Clue 2 then gives only-G

=17-10=7

Clue 3: only-L

=7+1=8

. Clue 1:

8=2x

, so

x=4

and

d+e=6

Clue 4 compares only-K with everyone enrolled in both K and L, which includes the 4 students in all three: only-K

=f+4

Total:

7+(f+4)+8+6+f+4=39

, so

f=5

and only-K

=9

Totals:

G=17

K=9+d+5+4=18+d

L=8+e+5+4=17+e

. Clue 5 (L is the largest) with

d=6-e

gives

17+e>24-e

, so

e\ge 4

and

d\le 2

The 4 triple-sport students each drop one sport:

p

leave G,

q

leave L and exactly 1 leaves K (K fell by one), so

p+q=3

After:

G=17-p

and

L=17+e-q

. The condition

G=L-6

gives

q-p=e-6

. With

p+q=3

q=\dfrac{e-3}{2}

Only

e=5

(from 4, 5, 6) makes

q

a whole number. So

e=5

d=1

q=1

and

p=2

After the withdrawal nobody is in all three sports. The students in both G and L are the

e=5

who were in G and L only, plus the 1 triple-sport student who dropped K and kept G and L:

5+1=6

Why Not the Others

A (7), C (5) and D (8) would each need a different value of

e

, but step 9 fixes

e=5

, with exactly one student dropping K.

Quick Check

Before:

7+9+8+1+5+5+4=39

, with

L=22>K=19>G=17

. After:

G=15

L=21

and

15=21-6

Correct Answer: B

Timed Practice

Attempt all of CAT 2018 Slot 2 DILR under the clock

The whole section, 60 minutes, in the TCS iON-style simulator. Free, no sign-up.

Start Free Test

CAT 2018 Slot 2 DILR at a Glance

Sets in this section8

Questions in this section32

Section time60 minutes

Convenor IIMIIM Calcutta

CAT 2018 Slot 2 DILR Set 8: Venn Diagrams (4 Questions) with Solutions

The Set: Read the Caselet First

Q29. Venn Diagrams

Q30. Venn Diagrams

Q31. Venn Diagrams

Q32. Venn Diagrams

Attempt all of CAT 2018 Slot 2 DILR under the clock

CAT 2018 Slot 2 DILR at a Glance

More CAT DILR Sets with Solutions

All sets in CAT 2018 Slot 2 DILR

Same type, other papers