GRE® Quant Practice | Set Theory Q5

The GRE maths sample question given below is a Select One or More Answers type question in Set Theory. This question tests the concept of Venn Diagrams and some fundamentals of Number Properties.

Question 5: In a group of people, n watched only La Liga and 2n watched EPL. If \\frac{\text{34}}{\text{n}}) watched both La Liga and EPL, how many watched La Liga?

1. 17
2. 21
3. 18
4. 19
5. 35
6. 36

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Video Explanation

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Explanatory Answer | GRE Set Theory Q5

Given Data
Number of people watching only La Liga = n
Number of People watching EPL = 2n
Number of people watching both La Liga and EPL = \\frac{\text{34}}{\text{n}})

Number of people watching is an integer.
So, \\frac{\text{34}}{\text{n}}) should be an integer.
If \\frac{\text{34}}{\text{n}}) is an integer, n has to be a factor of 34.
So, n can be 1, 2, 17 or 34.

If n = 1,
Number of people watching only La Liga = 1
Number of People watching EPL = 2
Number of people watching both La Liga and EPL = \\frac{\text{34}}{\text{1}}) = 34
Number of people watching EPL cannot be lesser than the number of people watching both EPL and La Liga.
The value of n cannot be 1.

If n = 2,
Number of people watching only La Liga = 2
Number of People watching EPL = 4
Number of people watching both La Liga and EPL = \\frac{\text{34}}{\text{2}}) = 17
Number of people watching EPL cannot be lesser than the number of people watching both EPL and La Liga.
The value of n cannot be 2.

If n = 17,
Number of people watching only La Liga = 17
Number of People watching EPL = 34
Number of people watching both La Liga and EPL = \\frac{\text{34}}{\text{17}}) = 2
Number of people watching La Liga = n + \\frac{\text{34}}{\text{17}}) = 17 + 2 = 19.

If n = 34,
Number of people watching only La Liga = 34
Number of People watching EPL = 68
Number of people watching both La Liga and EPL = \\frac{\text{34}}{\text{34}}) = 1
Number of people watching La Liga = n + \\frac{\text{34}}{\text{34}}) = 34 + 1 = 35.

Number of people who watched La Liga can be either 19 or 35.

Choices D and E are the correct answers