M14-19

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
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I think this question is good and helpful.

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.........

Please elaborate ??

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."

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

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

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.

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.

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.
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