求助：PREP模考上的一道DS题，希望一早起来就有神人解答，感恩~~~

wuyouyouuu

Did one of the 3 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.


答案是D： EACH statement ALONE is sufficient


好心人帮帮忙解释下（2）？？？？？？？

liangw

三个人，没有两个人卖的票数是一样的，也不可能有人卖负数张。如果一个人一张票没卖出，既0张，就不可能有第二个人卖0张。那么第二个人卖1张，第三个人就只能卖2张。。。所以满足。希望解释清楚了。。

SimingGMAT

楼上解释的很清楚~

附上Manhattan 上的解释。希望有帮助。
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.

wuyouyouuu

发现没看清题干~~谢谢解答了