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Among the first ten cyclists who crossed the finish-line, 4 [#permalink]
02 Mar 2009, 12:49

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Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1) 2 Italians who finished in the top ten did not represent Telefonica team

2) Each of the top ten finishers either was an Italian or represented Telefonica team or both

So you have 10 total spots to be filled. Here I would use the following equation: Total = Group 1 + Group 2 - Both + Neither

From the question, you are given the Total finishers, the number in group 1 (Italians) and number group 2(Telefonica Team)

Statement 1: 2 Italians who finished in the top ten did not represent the Telefonica team. This means 2 Italians did represent the telefonica team So... from our equation from before 10 = 4 + 8 -2 + Neither This is NOT Sufficient because we don't know how many people were members of the Telefonica Team and not Italians

Statement 2: Tells us that each of the top ten finishers was either an Italian or represented Telefonica or both. So we know there is no "neither" part to this equation. However we don't know how many Italians represented the Telefonica team.

It is given that 4 were Italians and 8 represented Telefonica team from a total of 10.

From stmt 1 = It is given that 2of the Italians were not Telefonica. If you draw a simple VENN Diagram, we know that

ONLY Italians = 2 Italians and Telefonica = 2 ONLY Telefonica = 6.

So sufficient.

From stmt2, it is given that each person is either Italian / represented Telefonica or both.

Applying the Union forumala, P(IUT) = P(I) + P(T) - P(I and T) ==> Solving it we get P(I and B) as 2. Drawing Simple Venn Diagram, we should be able to know ONLY Telefonica = 6. . So sufficient.

Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1) 2 Italians who finished in the top ten did not represent Telefonica team

2) Each of the top ten finishers either was an Italian or represented Telefonica team or both

Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1) 2 Italians who finished in the top ten did not represent Telefonica team

2) Each of the top ten finishers either was an Italian or represented Telefonica team or both

Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team. How many cyclists who represented Telefonica team and finished in the top ten were not Italians?

1) 2 Italians who finished in the top ten did not represent Telefonica team

2) Each of the top ten finishers either was an Italian or represented Telefonica team or both

xyz21 - That's how I got statement 1 to be sufficient.

I don't understand statement 2. What exactly is it saying and how do we translate that into the matrix?

Statement 2 is stating that each of the top ten players is either an Italian or represented Telefonica team. Hence there is no player who is neither Italian not represented Telephonica team.

So from xyz21's explanation matrix(4th one), we have a zero for the cell representing the Non Italian and Not Telefonica. But, since Not Italian is 6, it turns out that NOT Italian but Telephonica count will have to be 6.

xyz21 - That's how I got statement 1 to be sufficient.

I don't understand statement 2. What exactly is it saying and how do we translate that into the matrix?

Statement 2 is stating that each of the top ten players is either an Italian or represented Telefonica team. Hence there is no player who is neither Italian not represented Telephonica team.

So from xyz21's explanation matrix(4th one), we have a zero for the cell representing the Non Italian and Not Telefonica. But, since Not Italian is 6, it turns out that NOT Italian but Telephonica count will have to be 6.