# GRE® Quant Practice | Set Theory Q5

#### Select One or More Answers Question | Set Theory Question Bank

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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 ## Get to 170 in GRE Quant #### Online GRE Courses From INR 2999 ### Video Explanation ## GRE Live Online Classes #### Starts Mon, May 27, 2024 ### 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 #### GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GRE Live Online Classes Next Batch May 27, 2024 Work @ Wizako ##### How to reach Wizako? Mobile:$91) 93800 48484
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