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by GMATGuruNY » Sun Mar 27, 2016 3:27 pm
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
Statement 1:
If NONE of the members sells at least 2 tickets, then the 3 members sell a maximum of 1 ticket each, yielding the following total:
1+1+1 = 3.
Too small, since the total number of tickets sold = 6.
Implication:
For a total of 6 tickets to be sold, one of the 3 members must sell at least 2 tickets.
SUFFICIENT.

Statement 2:
LEAST possible case for the 3 members:
0 ticket, 1 ticket, 2 tickets.
The least possible case includes one member selling 2 tickets.
Implication:
For no two members to sell the same number of tickets, one of the 3 members must sell at least 2 tickets.
SUFFICIENT.

The correct answer is D.
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by neeti2711 » Fri Jul 22, 2016 8:03 am
Can't we assume that one member did not any ticket?
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by neeti2711 » Fri Jul 22, 2016 8:04 am
Can't we assume that one member did not any ticket? Since we are talking about a TEAM of 3 members - Can we replace "3 members" in statement 1 with "The Team"? I guess the answer will change then
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by DavidG@VeritasPrep » Fri Jul 22, 2016 8:25 am
neeti2711 wrote:Can't we assume that one member did not any ticket?

We can - Mitch actually considered that scenario when evaluating statement 2.

Statement two tells us that they all sold a different number of tickets.

The minimum that the first member sold: 0 tickets.
The minimum that the second member sold, given that this must be different than the number the first sold: 1 ticket.
The minimum that the third member sold, given that this must be different than the number the first two sold: 2 tickets.

Therefore we know that someone has to have sold at least two tickets.
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by neeti2711 » Fri Jul 22, 2016 9:34 am
Is there any specific knowledge required to solve this question? (May be about selling raffle tickets)

Why aren't we considering the possibility 1+1+4 or 0+2+4?
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by DavidG@VeritasPrep » Fri Jul 22, 2016 10:58 am
neeti2711 wrote:Is there any specific knowledge required to solve this question? (May be about selling raffle tickets)

Why aren't we considering the possibility 1+1+4 or 0+2+4?
For statement 1, you can consider those possibilities. But we're trying to determine if anyone sold at least two tickets. In both scenarios you've offered, the answer is YES, someone did sell at least two tickets. And no matter what scenario you consider to statement 1, the answer will always be YES, thus the statement is sufficient to answer the question. (Remember that sufficiency = consistency. If the answer to a YES/NO question is always YES, you have sufficiency. And if the answer is always NO you have sufficiency. It's when the answer could be YES or NO that a statement is not sufficient to answer the question.)
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