Set Theory Question

ganapathy.1989 wrote:How to approach question no.5(in the link below)?

https://docs.google.com/file/d/0B-S7r4r ... edit?pli=1

Data 1 is a ratio cum Venn diagram problem, which allegorically reads as under:

Maruti : Indigo = 4:3, Indigo : Alto = 2:3, therefore Maruti : Indigo : Alto = 8:6:9, and Maruti : Exactly Two = 2:1.

Refer to the Venn diagram attached and follow the coding, and let A, B, and C represent Maruti, Indigo, and Alto respectively.

Then, safe and sound A (100, 101, 110, 111) = 8, B (010, 011, 110, 111) = 6, and C (001, 011, 101, 111) = 9.

Also, (011, 101, 110) represent Exactly Two, such that Maruti : Exactly Two = 2:1 could suggest (011, 101, 110) = 4.

Data 1 also includes the ratio (111) : (110, 111) = 1:2, hence (110) = (111). To maximize the asked ratio, we need to maximize (111) in the Venn diagram.

We can eliminate the absurd choice (1), and for maximizing reasons, we can test the greatest of the remaining three choices. Let’s plug in choice (4) 5:6 for the asked ratio (111) : (100, 101) in the figure.

If (111) = (110) = 5, then we can have (100) = 4. (101) = 2, (001) = 10, (011) = 1, and (010) = 1, in the attached Venn diagram to show that 5:6 can fit to meet all conditions, hence best answer to question (5) of the link is choice [spoiler](4) 5:6[/spoiler].

Thank you sir. But I have a doubt. In the question it is given that the ratio of Maruti and (Indigo and Alto + Maruti and Alto) = 2:1 So effectively wont it be like (100,101,110,111) : (011+101) = 2:1 ?

ganapathy.1989 wrote:Thank you sir. But I have a doubt. In the question it is given that the ratio of Maruti and (Indigo and Alto + Maruti and Alto) = 2:1 So effectively wont it be like (100,101,110,111) : (011+101) = 2:1 ?

The phrase you underlined in the link means Exactly Two, hence it'd include all (011, 101, 110) and not just (011, 101).