Did one of the three members of a certain team

[Raj]

Did one of the three members of a certain team sell at least 2 raffle tickets yesterday?

(1) the 3 members sold a total of 6 raffle tickets yesterday
(2) No 2 of the members sold the same number of raffle tickets yesterday

During the test, I was confused with the way the problem was written. I did not clearly understand what "did one of the three" meant.

Anyways, I am thinking the question is asking if at least one of the three sell at least 2 tickets. With this assumption, I think this is the solution. Tutors, please correct if wrong

(1) if they sold 6 together, the possibilities (2,2,2), (1,2,3), (0,3,3) (different variations of these). In all cases, there is at least one with 2 or more.

(2). This I think is real cool.. if one of them is 0, the other is 1, the third one has to be 2 or more, hence sufficient.

Hence the answer is D.

I got this wrong in the exam.

-Raj.

[TakingGMAT]

1) Sufficient as even if 1 member sold 0 ticket, one member must have sold atleast 2 tickets as total sold tickets is 6.
2) Not sufficient because number of tickets sold is not given.

So answer should be B.
What is the correct answer.

[Raj]

Answer is D.

for 2), this is sort of tricky.. even if two of them sold the lowest possible 0 and 1, the third one has to sell at least 3 since they all sold different number of tickets. You dont actually have to know the total number. Hope that clarifies..
-Raj.

1) Sufficient as even if 1 member sold 0 ticket, one member must have sold atleast 2 tickets as total sold tickets is 6.
2) Not sufficient because number of tickets sold is not given.

So answer should be B.
What is the correct answer.

[RonPurewal]

yeah, this should be (d).

statement (1):
there's a statement called the pigeonhole principle, which basically says the following two things:
* if the AVERAGE of a set of integers is an INTEGER n, then at least one element of the set is > n.
* if the AVERAGE of a set of integers is a NON-INTEGER n, then at least one element of the set is > the next integer above n.
this principle is easy to prove: if you assume the contrary, then you get the absurd situation in which every element of a set is below the average of the set. that is of course impossible.

specifically, statement (1) is a case of the first part of the principle: the average of the set is 6/3 = 2, so at least one element of the set must be 2 or more.
again, you can prove this by reductio ad absurdum: if no one had sold 2 or more tickets, then you'd have a set in which everyone sold either 0 or 1 ticket, but the average is somehow still 2. that's untenable.

--

statement (2):
there are only two ways not to sell at least 2 tickets: sell 0 tickets, and sell 1 ticket.
if everyone sells a different # of tickets, then you can't fit three people into these two categories.
therefore, someone must have sold at least 2 tickets.

[AS24]

Hi Ron,

The question says "Did ONE of the members of a certain team sell AT LEAST 2 raffle tickets yesterday?" To me this means that the question is asking Did EXACTLY ONE of the members sell at least two tickets else the question would have been framed "did at least one of the members of a certain team sell at least 2 raffle tickets?" Apologies for mentioning this but sometimes you go wrong in answering questions because one word has changed the meaning of the question and when I do interpret the question in every detail it doesn't seem to be right.

Could you please clarify if my understanding is clearly an overinterpretation?

Thanks

[RonPurewal]

Hi Ron,

The question says "Did ONE of the members of a certain team sell AT LEAST 2 raffle tickets yesterday?" To me this means that the question is asking Did EXACTLY ONE of the members sell at least two tickets else the question would have been framed "did at least one of the members of a certain team sell at least 2 raffle tickets?" Apologies for mentioning this but sometimes you go wrong in answering questions because one word has changed the meaning of the question and when I do interpret the question in every detail it doesn't seem to be right.

Could you please clarify if my understanding is clearly an overinterpretation?

Thanks

i do see your point"”i.e., i see how you could have interpreted the statement in that way.

however, in this particular instance, the context (= the correct answer) makes it clear that "did one of the..." refers to at least one of the team members. so, you should absorb that lesson as a takeaway for similarly worded problems in the future.

(if the statement had the meaning that you attributed to it here, then the answer would be (e).
if you interpret the question as "Did exactly one of ...?", then (0, 1, 5) and (1, 2, 3) satisfy both statements, but (0, 1, 5) would be a yes to your version of the question and (1, 2, 3) would be a no.)