CAT 2024 Slot 1 · DILR · Question 19

Solving the set

Step 1 – Read the chart.

Traveller	Asia	Europe	ROW	Total
Dheeraj	3	7	1	11
Samantha	0	9	4	13
Nitesh	1	6	12	19
Total	4	22	17	43

Step 2 – Count countries visited by exactly two people. Adding the three individual totals counts a country once for each person who visited it: 43 = (visited by one) + 2 × (by two) + 3 × (by three). With 32 countries in all, 43 − 32 = 11 = (by two) + 2 × (by three). Only USA was visited by all three, so countries visited by exactly two = 11 − 2 = 9.

Step 3 – Split these 9 by pair.

• Dheeraj and Nitesh only: China only (fact 3) → 1.

• Dheeraj and Samantha only: Samantha visited no Asian country, so the only such country is France (fact 4) → 1.

• Samantha and Nitesh only: 9 − 1 − 1 = 7.

Step 4 – Fact 5. Samantha and Nitesh together visited 7 + 1 (USA) = 8 countries, so 4 are in Europe. The other 4 are not in Asia (Samantha visited none), so they are in ROW: USA + 3 others.

Step 5 – Region by region.

• Asia: Samantha 0. Nitesh's only Asian country is China, which Dheeraj also visited. Dheeraj's other 2 Asian countries are his alone. Asia total = 3.

• Europe: Dheeraj 7 = France + 6 alone. Samantha 9 = France + 4 (with Nitesh) + 4 alone. Nitesh 6 = 4 (with Samantha) + 2 alone. Europe total = 6 + 4 + 2 + 1 + 4 = 17.

• ROW: Dheeraj 1 = USA. Samantha 4 = USA + 3 (with Nitesh). Nitesh 12 = USA + 3 + 8 alone. ROW total = 1 + 3 + 8 = 12.

Check: 3 + 17 + 12 = 32, which matches fact 1.

Category	Asia	Europe	ROW	Total
All three (D, S, N)	0	0	1 (USA)	1
D and N only	1 (China)	0	0	1
D and S only	0	1 (France)	0	1
S and N only	0	4	3	7
Only Dheeraj	2	6	0	8
Only Samantha	0	4	0	4
Only Nitesh	0	2	8	10
Visited by at least one	3	17	12	32

This question

From Step 5, the countries in Asia are Dheeraj's 3 countries (including China, also visited by Nitesh). Samantha visited none, and Nitesh's only Asian country is China.

So 3 countries in Asia were visited by at least one of them.

Hence, the answer is 3.