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Did one of the 3 members of a certain team sell at least 2 [#permalink]

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04 Aug 2012, 10:18

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Question Stats:

54% (01:45) correct
46% (00:49) wrong based on 258 sessions

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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.

Acc to (1) one should mean only 1 member sold atleast 2 raffle, NOT atleast one member sold atleast 2 raffle. Hence, the two contradictory options should be : 0,0,6- one member sold atleast 2 raffle 2,2,2- more than one member sold atleast 2 raffle.

Did one of the 3 members of a certain team sell at least 2 raffle tickets yesterday?

The question basically asks whether there is a member who sold at least 2 tickets (so 2 or more).

(1) The 3 members sold a total of 6 raffle tickets yesterday. If each of the 3 members sold less than 2 tickets, then the total # of tickets sold cannot be 6, hence at least one member sold at least 2 tickets. Sufficient.

Or: can we split 6 tickets so that ALL 3 members to have sold less than 2 tickets? No: (6,0,0); (5,1,0), (4,1,1); (4,2,0); (3,3,0),(3,2,1), (2,2,2). Sufficient.

(2) No 2 of the members sold the same number of raffle tickets yesterday. If one member sold 0 tickets and another sold 1 ticket (the least possible numbers), then the third one must have sold more than 1, so 2 or more. Sufficient.

Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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04 Aug 2012, 10:50

Bunuel wrote:

Did one of the 3 members of a certain team sell at least 2 raffle tickets yesterday?

The question basically asks whether there is a member who sold at least 2 tickets (so 2 or more).

(1) The 3 members sold a total of 6 raffle tickets yesterday. If each of the 3 members sold less than 2 tickets, then the total # of tickets sold cannot be 6, hence at least one member sold at least 2 tickets. Sufficient.

Or: can we split 6 tickets so that ALL 3 members to have sold less than 2 tickets? No: (6,0,0); (5,1,0), (4,1,1); (4,2,0); (3,3,0),(3,2,1), (2,2,2). Sufficient.

(2) No 2 of the members sold the same number of raffle tickets yesterday. If one member sold 0 tickets and another sold 1 ticket (the least possible numbers), then the third one must have sold more than 1, so 2 or more. Sufficient.

Answer: D.

Hope it's clear.

If the Q asks "whether there is a member who sold at least 2 tickets (so 2 or more)" then it should have been framed as atleast one NOT one which indicates Exactly one. Hence the doubt. Infact, i would say the Q should use the word Atleast or Exactly to make it clear.

Did one of the 3 members of a certain team sell at least 2 raffle tickets yesterday?

The question basically asks whether there is a member who sold at least 2 tickets (so 2 or more).

(1) The 3 members sold a total of 6 raffle tickets yesterday. If each of the 3 members sold less than 2 tickets, then the total # of tickets sold cannot be 6, hence at least one member sold at least 2 tickets. Sufficient.

Or: can we split 6 tickets so that ALL 3 members to have sold less than 2 tickets? No: (6,0,0); (5,1,0), (4,1,1); (4,2,0); (3,3,0),(3,2,1), (2,2,2). Sufficient.

(2) No 2 of the members sold the same number of raffle tickets yesterday. If one member sold 0 tickets and another sold 1 ticket (the least possible numbers), then the third one must have sold more than 1, so 2 or more. Sufficient.

Answer: D.

Hope it's clear.

If the Q asks "whether there is a member who sold at least 2 tickets (so 2 or more)" then it should have been framed as atleast one NOT one which indicates Exactly one. Hence the doubt. Infact, i would say the Q should use the word Atleast or Exactly to make it clear.

Not so (even though I do see why you are confused).

Actually it's opposite, if the question meant exactly (only) one, then it would say so.
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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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28 Oct 2013, 13:53

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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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17 Sep 2015, 05:54

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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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26 Oct 2016, 04:05

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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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29 Nov 2016, 20:45

The question looks kind of tricky to me, However deep diving I think- the bottomline of the question is did any of the 3 members sold more than 1 ticket.

Now total no of tickets sold in 6 and tickets cannot be negative or fractions hence yes statement 1 is true.

Similarly statement 2 is also true if 3 of them sold different number of tickets then they can sell (0,1, 2) tickets .

Thus both the statements are sufficient to prove it correct.

Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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02 Feb 2017, 18:35

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.

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.

Re: Did one of the 3 members of a certain team sell atleast 2 raffle ticke [#permalink]

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10 Feb 2017, 23:33

ram186 wrote:

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

(1) 3 members sold a total of 6 raffle tickets - Combinations are 2,2,2, 4,1,1, 5,0,1, and so on. So in each case at least one would've sold more than 2. - Sufficient

(2) No 2 of the members sold the same number of raffle tickets yesterday - We don't know how many tickets were sold yesterday but we know no 2 person sold the same no. of tickets. Since they are tickets they must be 3 different non negative integers. The 2 different smallest non negative integers are 0, and 1. Hence the other one has to be either 2 or greater than 2. So either way we can tell one person has sold at least 2 raffle tickets. - Sufficient

Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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11 Feb 2017, 11:54

Sure. This is a good alternative solution.

But will you really remember this principle on the test day ?

In my opinion, it's better to go intuitive about questions. But that's what I think. Everyone's got his/her way of doing things !

anairamitch1804 wrote:

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.

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.

Hence D.

gmatclubot

Re: Did one of the 3 members of a certain team sell at least 2
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11 Feb 2017, 11:54

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