CAT 2024 Slot 1 · DILR · Set 5: Countries Visited by Dheeraj, Samantha and Nitesh

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.

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, Nitesh visited 6 European countries: 4 shared with Samantha and 2 visited by him alone. He shares no European country with Dheeraj, because China is his only country shared with Dheeraj but not Samantha, and USA is the only country visited by all three.

So 2 countries in Europe were visited only by Nitesh.

Hence, the answer is 2.

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 4, Samantha and Nitesh together visited 8 countries: 4 in Europe and 4 in ROW (USA and 3 others).

So 4 countries in the ROW were visited by both of them.

Hence, the answer is 4.

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, in Europe: only Dheeraj = 6, only Samantha = 4, only Nitesh = 2.

Countries in Europe visited by exactly one of them = 6 + 4 + 2 = 12.

Hence, the answer is option 2.