CAT 2024 Slot 1 DILR Set 2 Q5–Q8

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2024 Slot 1, with 4 questions (Venn & Set Puzzles). Answers are CAT's official key.

The set

This set relies on a figure in the original paper, which is not reproduced here. The questions and answers are below.

The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW).

[Figure in the original paper]
The following additional facts are known about the countries visited by them.

1. 32 countries were visited by at least one of them.
2. USA (in ROW) is the only country that was visited by all three of them.
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
5. Half of the countries visited by both Samantha and Nitesh are in Europe.

Question 5

How many countries in Asia were visited by at least one of Dheeraj, Samantha and Nitesh?

TITA: type in the answer. There are no options and no negative marking.

Answer: 3 Venn & Set Puzzles TITA

Solution

  1. Total visits \(= (3+7+1) + (0+9+4) + (1+6+12) = 43\), and 32 distinct countries were visited. The extra \(43 - 32 = 11\) equals (countries in exactly two lists) \(+ 2 \times\) (countries in all three).
  2. Only USA is in all three, which accounts for 2. Dheeraj and Nitesh only: China (1). Dheeraj and Samantha only: France (1), since Samantha visited no Asian country. So Samantha and Nitesh only \(= 11 - 2 - 1 - 1 = 7\), and Samantha \(\cap\) Nitesh \(= 8\) including USA.
  3. Half of those 8, that is 4, are in Europe. The other 4 are in ROW: USA plus 3 more.
  4. Europe: Dheeraj 7 (France shared with Samantha), Samantha 9 (France plus 4 shared with Nitesh), Nitesh 6 (4 shared with Samantha). So only-D \(= 6\), only-S \(= 4\), only-N \(= 2\). Asia: Dheeraj 3, Nitesh 1 (China, also Dheeraj's), Samantha 0.
  5. Asia: Dheeraj's 3 countries include China, which is Nitesh's only Asian country, and Samantha has none. So the union is 3.

Shortcut. Nitesh's single Asian country is China, which Dheeraj also visited, so the union is just Dheeraj's 3.

Question 6

How many countries in Europe were visited only by Nitesh?

TITA: type in the answer. There are no options and no negative marking.

Answer: 2 Venn & Set Puzzles TITA

Solution

  1. Total visits \(= (3+7+1) + (0+9+4) + (1+6+12) = 43\), and 32 distinct countries were visited. The extra \(43 - 32 = 11\) equals (countries in exactly two lists) \(+ 2 \times\) (countries in all three).
  2. Only USA is in all three, which accounts for 2. Dheeraj and Nitesh only: China (1). Dheeraj and Samantha only: France (1), since Samantha visited no Asian country. So Samantha and Nitesh only \(= 11 - 2 - 1 - 1 = 7\), and Samantha \(\cap\) Nitesh \(= 8\) including USA.
  3. Half of those 8, that is 4, are in Europe. The other 4 are in ROW: USA plus 3 more.
  4. Europe: Dheeraj 7 (France shared with Samantha), Samantha 9 (France plus 4 shared with Nitesh), Nitesh 6 (4 shared with Samantha). So only-D \(= 6\), only-S \(= 4\), only-N \(= 2\). Asia: Dheeraj 3, Nitesh 1 (China, also Dheeraj's), Samantha 0.
  5. Nitesh's 6 European countries include the 4 shared with Samantha. None is shared with Dheeraj (Dheeraj and Nitesh share only China and USA). So \(6 - 4 = 2\) were visited only by Nitesh.

Question 7

How many countries in the ROW were visited by both Nitesh and Samantha?

TITA: type in the answer. There are no options and no negative marking.

Answer: 4 Venn & Set Puzzles TITA

Solution

  1. Total visits \(= (3+7+1) + (0+9+4) + (1+6+12) = 43\), and 32 distinct countries were visited. The extra \(43 - 32 = 11\) equals (countries in exactly two lists) \(+ 2 \times\) (countries in all three).
  2. Only USA is in all three, which accounts for 2. Dheeraj and Nitesh only: China (1). Dheeraj and Samantha only: France (1), since Samantha visited no Asian country. So Samantha and Nitesh only \(= 11 - 2 - 1 - 1 = 7\), and Samantha \(\cap\) Nitesh \(= 8\) including USA.
  3. Half of those 8, that is 4, are in Europe. The other 4 are in ROW: USA plus 3 more.
  4. Europe: Dheeraj 7 (France shared with Samantha), Samantha 9 (France plus 4 shared with Nitesh), Nitesh 6 (4 shared with Samantha). So only-D \(= 6\), only-S \(= 4\), only-N \(= 2\). Asia: Dheeraj 3, Nitesh 1 (China, also Dheeraj's), Samantha 0.
  5. Samantha \(\cap\) Nitesh in ROW \(= 8 - 4 = 4\) (USA plus 3 others).

Question 8

How many countries in Europe were visited by exactly one of Dheeraj, Samantha and Nitesh?
  1. A
    12
  2. B
    14
  3. C
    10
  4. D
    5

Answer: (A) 12 Venn & Set Puzzles MCQ

Solution

  1. Total visits \(= (3+7+1) + (0+9+4) + (1+6+12) = 43\), and 32 distinct countries were visited. The extra \(43 - 32 = 11\) equals (countries in exactly two lists) \(+ 2 \times\) (countries in all three).
  2. Only USA is in all three, which accounts for 2. Dheeraj and Nitesh only: China (1). Dheeraj and Samantha only: France (1), since Samantha visited no Asian country. So Samantha and Nitesh only \(= 11 - 2 - 1 - 1 = 7\), and Samantha \(\cap\) Nitesh \(= 8\) including USA.
  3. Half of those 8, that is 4, are in Europe. The other 4 are in ROW: USA plus 3 more.
  4. Europe: Dheeraj 7 (France shared with Samantha), Samantha 9 (France plus 4 shared with Nitesh), Nitesh 6 (4 shared with Samantha). So only-D \(= 6\), only-S \(= 4\), only-N \(= 2\). Asia: Dheeraj 3, Nitesh 1 (China, also Dheeraj's), Samantha 0.
  5. Exactly one in Europe \(= 6 + 4 + 2 = 12\).

Same concept in other years

See every question on Venn diagram: counts of items belonging to overlapping categories (3-4 sets).

More Venn & Set Puzzles questions from CAT

All 60 Venn & Set Puzzles questions asked since 2017.