CAT 2024 Slot 1DILR Question 15

3 SetsEasy
Passage / Data

Answer the following questions based on the information given 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).

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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.

How many countries in Europe were visited only by Nitesh?

Answer & solution

Answer: 2

Solution

Hard

Chart: Dheeraj (A3, E7, R1), Samantha (A0, E9, R4), Nitesh (A1, E6, R12). From inclusion–exclusion with triple t=1t=1: a+b+c=9a+b+c=9; b=1b=1 (China), a=1a=1 (France), c=7c=7, so SN=8|S\cap N|=8 with 4 of them in Europe.

1

Strip Nitesh’s shared Europe countries. France is D&S (not Nitesh), China (D&N) is in Asia, and there is no triple in Europe — so only the S&N overlap matters.

Nitesh Europe=6(chart) shared with Samantha=4(set-up) only Nitesh=64=2\begin{aligned} &\text{Nitesh Europe}=6 \quad\text{(chart)}\\ &\Rightarrow\ \text{shared with Samantha}=4 \quad\text{(set-up)}\\ &\Rightarrow\ \text{only Nitesh}=6-4=2 \end{aligned}
2 countries\mathbf{2}\ \text{countries}
CAT 2024 Slot 1 DILR Q15: How many countries in Europe were visited only by Nitesh? — Solution | TheCATExam