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Did one of the 3 members of a certain team sell at least 2
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Updated on: 25 Jun 2017, 04:59
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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.
Please explain why should D be the answer. This is a Q from GMAT Prep with D as answer, please take notice.
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Originally posted by saurabhkhatrinitk on 04 Aug 2012, 09:18.
Last edited by hazelnut on 25 Jun 2017, 04:59, edited 3 times in total.
EDITED THE QUESTION.




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Re: Did one of the 3 members of a certain team sell at least 2
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04 Aug 2012, 09:40
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.
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Re: Did one of the 3 members of a certain team sell at least 2
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04 Aug 2012, 09:50
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.



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Re: Did one of the 3 members of a certain team sell at least 2
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04 Aug 2012, 11:44
saurabhkhatrinitk wrote: 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. 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
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29 Nov 2016, 19:45
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.
Hope this helps.



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Re: Did one of the 3 members of a certain team sell at least 2
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02 Feb 2017, 17:35
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 NONINTEGER 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.
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Re: Did one of the 3 members of a certain team sell at least 2
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10 Feb 2017, 22:33
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 Hope this explains. Cheers!



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Re: Did one of the 3 members of a certain team sell at least 2
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11 Feb 2017, 10:54
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 NONINTEGER 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.



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Did one of the 3 members of a certain team sell at least 2
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16 Aug 2017, 02:02
I agree with some people who posted their doubts about the questions earlier. I chose option E.
If the question had clearly mentioned "Did atleast one of the 3 members of a certain team sell at least 2 raffle tickets yesterday." then it would've caused much less confusion.
But at the end of the day it's an official question, so we can't argue much. :/



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Re: Did one of the 3 members of a certain team sell at least 2
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31 Oct 2018, 12:35
saurabhkhatrinitk 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.
\(A,B,C\, \ge 0\,\,{\rm{ints}}\,\,\,\left( * \right)\) \(?\,\,\,:\,\,\,\,A \ge 2\,\,\,{\rm{or}}\,\,\,B \ge 2\,\,\,{\rm{or}}\,\,\,C \ge 2\) \(\left( 1 \right)\,\,A + B + C = 6\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\) \(\left( {**} \right)\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\left\{ \matrix{ \,A \le \,\,1 \hfill \cr \,B \le \,\,1 \hfill \cr \,C \le \,\,1 \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,A + B + C\,\, \le \,\,3\,\,\,\,\, \Rightarrow \,\,\,\,\left( 1 \right)\,\,\,{\rm{contradicted}}\) \(\left( 2 \right)\,\,A,B,C\,\,{\rm{different}}\,\,\,\,\mathop \Rightarrow \limits^{\left( {***} \right)} \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\) \(\left( {***} \right)\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,A \le \,\,1\,\,\,\, \Rightarrow \,\,\,A \in \left\{ {0,1} \right\} \hfill \cr \,B \le \,\,1\,\,\,\, \Rightarrow \,\,\,B \in \left\{ {0,1} \right\} \hfill \cr \,C \le \,\,1\,\,\,\, \Rightarrow \,\,\,C \in \left\{ {0,1} \right\} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( 2 \right)\,\,\,{\rm{contradicted}}\,\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
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Re: Did one of the 3 members of a certain team sell at least 2
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16 Nov 2018, 08:29
(1) The 3 members sold a total of 6 raffle tickets yesterday. Minimum case = 2 each by 3 members other cases 0,0,6 or 1,0,5 and many more in all at least one has sold 2 tickets (2) No 2 of the members sold the same number of raffle tickets yesterday. Minimum case  0,1,5 or 1,2,3 or 0,2,4 0r any other Tickets will always be at least 2 for one of member as case 2,2,2 is not valid here So answer is D
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