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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

Re: GMATCLUB M14#19 [#permalink]
02 Feb 2009, 21:27

topmbaseeker wrote:

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

(C) 2008 GMAT Club - m14#19

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

A is the best

10=4+8-x, x=2, so the cyclists who were not Italians are 8-2=6, suff _________________

[X][X][X][X][X][X][X][X][X][X] - 4 of 10 are Italians [X][X][X][X][X][X][X][X][X][X] - 8 of 10 are Telefonica cyclists.

In this example, 2 cyclists represent neither Italians, nor Telefonica ([X]-[X] combinations) 4 cyclists are Italians and represents Telefonica ([X]-[X] combinations) 4 cyclists aren't Italians and represents Telefonica ([X]-[X] combinations)

1) Now, let's consider first condition: 2 Italians who finished in the top ten did not represent Telefonica team We should cover 2 not Telefonica cyclists: [X][X]................................... [X][X][X][X][X][X][X][X][X][X] It is obvious that other 2 Italians belongs Telefonica team (there are no other options). Therefore, the number of cyclists who represented Telefonica team and were not Italians is 8-2=6. Sufficient.

2) Now, let's consider second condition: Each of the top ten finishers either was an Italian or represented Telefonica team or both And again we should cover 2 not Telefonica cyclists. Otherwise, not Italian and not Telefonica cyclist would be possible contradicting second condition: [X][X]................................... [X][X][X][X][X][X][X][X][X][X] The same reasoning as for first condition. Sufficient.

I've tried to make my reasoning as clear as I could. In fact, it is fast 10-20 sec method. _________________

If 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.

1) The statement is a bit cryptic, but what it means is - 2 Italian's were not a part of T and the other 2 were(4 Italians won in top 10) : 8-2= 6 T's Not I's 2) Use Set Theory: n(aUb)=n(a) + n(b) - n(aOb) : O=Intersection. We are given n(a), n(b) and n(aUb) - Calc n(aOb) : n(aOb)=2 => b(only)= n(b)-n(aOb)=6

This is being made more complicated than it needs to be. You don't need any formulas.

(1) We already know 8 of the 10 are part of Telefonica. (1) tells us the other two were both italian, so that acounts for all 10. The other two italians had to represent Telefonica. Suff (2) Basicallay the same as (1). If all 10 were italian, part of Telephinica or both, then the 2 non-telefonica people had to be italian. Suff

Stmt 1 suffice that 2 are italians & not in Telefonica team. so 6 Telefonica team members are not italian & in top ten.

to Prove Stmt 2:

p(AUB)=p(A)+p(B) -p(AintersectionB)

P(AUB)=10 P(A)=8 P(B)=4 thus p(AintersectionB)=2 which gives the number of italians not in telefonica & thus we can conclude that 6 telefonica are not italian.

what is stopping me from saying that there are 4 italians that are part of the 8 telefonica team, and there are 2 who finished top ten who are non telefonica?

Because the original statement says "Among the first ten cyclists who crossed the finish-line, 4 were Italians and 8 represented Telefonica team." There are only 4 italians. If there were 4 that were part of the telefonica team, and 2 that were not, then there would be 6 italians altogether.

D , each statement alone sufficient as 1) 2 Italians who finished in the top ten did not represent Telefonica team out of 4 , 2 were were both telefonica and italian ,so 8-2 = 6 were solely Telefonica sufficient

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

Friends, I am newbie here so sorry if i am acting stupid by replying this. In my openion B will be the correct answer. (2) says that Each of the top ten finishers either was an Italian or represented Telefonica team or both. With help of 2) you can say that 10 winners = 4 italians + 8 Telephonica i.e., 2 are both italians and Teliphonica. so, 2 alone is sufficiant. Now, (1) says that "2 Italians who finished in the top ten did not represent Telefonica team" but it does not say that there is no third category of winners for examples french, or german. so (1) alone is not enough. Please correct me if i am wrong

Friends, I am newbie here so sorry if i am acting stupid by replying this. In my openion B will be the correct answer. (2) says that Each of the top ten finishers either was an Italian or represented Telefonica team or both. With help of 2) you can say that 10 winners = 4 italians + 8 Telephonica i.e., 2 are both italians and Teliphonica. so, 2 alone is sufficiant.

Now, (1) says that "2 Italians who finished in the top ten did not represent Telefonica team" but it does not say that there is no third category of winners for examples french, or german. so (1) alone is not enough. Please correct me if i am wrong

Welcome! Do not apologize. Questions are the best kinds of posts.

Do not concern yourself with other nationalities. There are other nationalities of course, as there are only 4 italians, there must be 6 non-italians, which could be french, german, etc. If there were 10 finishers, and 8 of those 10 represented Telefonica, and 2 did not represent Telefonica, then that accounts for all 10. The statement says that 2 italians did not rep Telefonica, and since there are only 4 italians total, the other 2 did rep Telefonica. I hope this helps. Please continue to ask questions.

If 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?

2 Italians who finished in the top ten did not represent Telefonica team. Each of the top ten finishers either was an Italian or represented Telefonica team or both. (C) 2008 GMAT Club

How can we assume that in the top 10 there were no non-italian AND non-telefonica participants?source is gmat club tests m14...

Given: Total = 10; Italian = 4; Telefonica = 8 Only Tele = Tele - Both So, rephrase question is: what is Both?

We can use the following: Total - Neither = Italian + Tele - Both Italian = Only Italian + Both => Both = Italian - Only Italian

So, if Only Italian is known, we can find Both and subsequently can find Only Tele.

S1: Only Italian = 2: So Both = Italian - Only Italian = 4 - 2 => Both = 2 Therefore: Only Tele = Tele - Both = 8 - 2 = 6 So, S1 is sufficient.

S2: If Total = Italian + Tele - Both; Neither = 0 Using Total - Neither = Italian + Tele - Both => 10 - 0 = 8 + 4 - Both => Both = 2 So, S2 is sufficient.

If 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 --> since 2 Italians did not represent Telefonica team then remaining 2 Italians did represent Telefonica team, hence out of 8 cyclists who represented Telefonica team 8-2=6 were not Italians. Sufficient.

(2) Each of the top ten finishers either was an Italian or represented Telefonica team or both --> Total=Italians +Telefonica-Both --> 10=4+8-Both --> Both=2. So, 2 cyclists represented Telefonica and were Italians, which means that 8-2=6 cyclists represented Telefonica but were not Italians. Sufficient.