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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 Source: GMAT Club Tests - hardest GMAT questions
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Re: GMATCLUB M14#19 [#permalink]
 02 Feb 2009, 22:27
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
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Re: GMATCLUB M14#19 [#permalink]
03 Feb 2009, 02:14
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DLet's imagine how it would be: [X] - unknown cyclist. [X] - Italian [X] - Telefonica team's cyclist. [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.
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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
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I = Italian NI = Not Italian T = represents Telefonica team NT = does not represent Telefonica
Attachments
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Out of 10 memebers
4 were Italian 8 represents telefonica
from condition 1
10=2(I)+2(I+T)+6T
6 members represents telefonica and are not italians
from condition 2
only one possibility
Each members either italian or Represents telefonica or both
I I I+T I+T T T T T T T
I think answer is D
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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
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Ans is D.
Reason:
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.
Thus D is right Ans.
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ksharma12 wrote: For Statement 2,
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.
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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
let both be x
4+8-x = 10
x=2
8-2 =6
suffcient
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its more of a 2-elements (Italian & Telefonica) set question. from stmt2: 2 strictly Italians; 2 both Italians and Telefonica, and 6 Telefonica- non Italians.
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Ans:D From S1: I=4 out of this 2 Italian. so, 2I+XT+2IT=10 so 6T S2:Total=I+T-IT ,10=4+8-IT,now same as S1 we can find ans.
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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
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amitjash wrote: 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.
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Attachment: 
2010-10-28_195326.png [ 4.41 KiB | Viewed 3142 times ]
2) is so tricky! - it is just saying that there are no such guys who are not italians and not represent telefonica , so you must take it as =0. Here is my representation, where in blue are calculations based on 1) and in green calculations based on 2).
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10 = I + T - both So T - both = ? (1) I - both = 2 => both = 4 - 2 = 2 So T - both = 8 - 2 = 6 (1) is sufficient (2) 10 = 4 + 8 - both => both = 2 So only T = 8 -2 = 6 (2) is sufficient Answer - D
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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...
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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.
Correct answer is D.
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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. Answer: D.
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