M14-19

Question

In the top ten finishers of a cycling race, 4 were Italians and 8 represented the Telefonica team. How many cyclists from the Telefonica team in the top ten were not Italian?

(1) 2 of the top ten finishers who were Italian did not represent the Telefonica team.
 
(2) Every cyclist who finished in the top ten was either Italian, represented Telefonica team, or both.

Bunuel · Accepted Answer

Official Solution:

In the top ten finishers of a cycling race, 4 were Italians and 8 represented the Telefonica team. How many cyclists from the Telefonica team in the top ten were not Italian? 
 
(1) 2 of the top ten finishers who were Italian did not represent the Telefonica team.
 
Since 2 out of the 4 Italians in the top 10 did not represent the Telefonica team, it follows that the remaining 2 Italians must have been part of the Telefonica team. Thus, out of the 8 cyclists who represented the Telefonica team, 8 - 2 = 6 were not Italians. Therefore, statement (1) is sufficient.
 
(2) Every cyclist who finished in the top ten was either Italian, represented Telefonica team, or both.
 
The given statement implies that there were no cyclists in the top 10 who were neither Italian nor representing the Telefonica team. Using the formula  \{Total\} = \{Italians\} + \{Telefonica\} - \{Both\} , we can find that  \{Both\} = 2 . Since 2 of the top finishers were both Italian and representing Telefonica teams, there were 8 - 2 = 6 top finishers who represented Telefonica but were not Italian. Thus, statement (2) is also sufficient to answer the question.

Answer: D

ppac · Answer

I think this question is  good  and  helpful .

manish8383 · Answer

Why Stat.1 is Sufficient ? It is only statement 2 that complete the question by stating the actual type of participants i.e. either Italian or Telefonica or both and no one else. Stat 1...gives Quantity Stat 2....gives Type Stat 1+2 gives OA....C......... :roll:

Please elaborate ??

shasadou · Answer

Hi

I have compiled a small matrix box because this tool is the best to most overlapping sets problems - venn diag are ambigious for me.

NOTE: we do not need to know for the Statement 1 whether there is a "NONE" GROUP - YOU WILL SEE IN THE MATRIX. Statement 2 virtually states that there is none of "NONE" because everyone belongs either to both sets or at least to one of the sets:

"Each of the top ten finishers either was an Italian or represented Telefonica team or both."

karanchamp1 · Answer

my solution:
1)gives c=2 so
 a=4-c=2 
 d=2-c=0
 b=8-a or b=6-d so b=6 
SUFFICIENT
2) gives d=0 use b+d=6 to get b=6
SUFFICIENT
ANSWER: D

grsm · Answer

I think this is a  high-quality  question and I agree with explanation. this is a very good question!

Cbirole · Answer

I think this is a  high-quality  question and I agree with explanation.

Sunil7k · Answer

The formula valid here is 
 Total-Neither = A + B -Both

From Question stem.. we can infer following details:- 
Total =10,
Italian (A) = 4
Telifonica Team (B) = 8

Statement 1  : Both (overlapping part)= 2 ,
so, Total-Neither = A + B -Both
Neither = Total-(A+B)+ Both
Neither = 10-(4+8) + 2
Neither = 0.
So required value = B-both= 8-2= 6.
Hence Sufficient.

Statement 2  :
Value of Neither is given, i.e 0 .. So here one can infer Value of "Both"(overlapping part)

so, Total-Neither = A + B -Both
10-0=4+8-Both
Both=2
So required value = B-both= 8-2= 6.
Hence Sufficient.

rickyric395 · Answer

Hi  Bunuel , for statement 1 to be correct, we have to assume that 10 winners exclusively comprised of only Telefonica team or Italians or both, but it is not explicitly mentioned anywhere.

Bunuel · Answer

No. If 2 out of the 4 Italians in the top 10 did NOT represent the Telefonica team, then the remaining 2 Italians must have been part of the Telefonica team. How else ? Thus, out of the 8 cyclists who represented the Telefonica team, 8 - 2 = 6 were not Italians. Therefore, statement (1) is sufficient.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

toan999 · Answer

I don’t quite agree with the solution. When i read the statement (2), I thought that you want to confirm that there are no other teams or nationalities so we can solve it by overlapping set.

Bunuel · Answer

That’s wrong. The line “Every cyclist who finished in the top ten was either Italian, represented Telefonica, or both” already defines the complete set of top-ten cyclists. It doesn’t just exclude others but tells you exactly how the two groups (Italians and Telefonica) cover all ten. That’s why you can immediately apply the overlap relation Total = Italians + Telefonica - Both, find Both = 2, and get the correct answer.

toan999 · Answer

Agree, but what I mean is that in that case the statement (1) is not enough because there may be another team. So the answer should be B.

Bunuel · Answer

The answer should be and is D. Statement (1) alone is sufficient because it tells us that 2 Italians are not in the Telefonica team, so the remaining 2 Italians are. That means in the top 10, 2 Italians are part of Telefonica. Since there are 8 Telefonica cyclists in total, 8 - 2 = 6 of them are not Italian. The presence of other teams does not affect this, as the question is limited to Italians and Telefonica members in the top ten. Please review the question carefully.

RishabhChowdhury · Answer

Hey there!
Good day!
I had a quick question regarding this problem.
I did come up with the stated solution, but I rejected Statement 2 in the end.
My understanding is that Statement 2 doesn't seem to adequately address the possibility that all 4 Italians could be part of Telefonica team or maybe 3 out of the 4 Italians could be part of the Telefonica team.
Is my understanding incorrect? Could you please correct me if I'm wrong and help me understand?

Bunuel · Answer

I think your doubt is addressed in this thread. Please review and let me know if still unclear.

M14-19

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