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# Did one of the 3 members of a certain team sell atleast 2

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

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11 Mar 2009, 18:18
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55% (hard)

Question Stats:

51% (01:22) correct 49% (00:23) wrong based on 417 sessions

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Did one of the 3 members of a certain team sell atleast 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: did-one-of-the-3-members-of-a-certain-team-sell-at-least-136811.html
[Reveal] Spoiler: OA
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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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13 Jul 2010, 22:08
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1. Sufficient.

Cases : (0,0,6), (0,1,5),(0,2,4),(2,2,2),(1,2,3) etc All add upto 6. So one of the member sold atleast 2 tickets.

2. Sufficient.

Lets look at the min number of tickets that can be sold (when all the three are unequal)

M1 0
M2 1
M3 2

M3 sold atleast 2 tickets.

Hence D.
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Re: DS -gmatprep1 -- raffle tickets [#permalink]

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11 Mar 2009, 20:23
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Given:

stmt 1:

3 members sold a total of 6 raffel tickets.
on a average each should sell 2 tickets.
So it can be (2,2,2);(1,2,3);(4,1,1).
So one of the 3 members will definetly sell atleast 2 raffel tickets.
Therefore sufficient .

stmt2 :
No two members sold the same number of raffel tickets.
giving the lowest possible value ( 0,1,2);(1,2,3). Therefore sufficient.

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

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13 Jul 2010, 19:28
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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 tickets yesterday
(2) No 2 members sold the same number of tickets

Last edited by Bunuel on 17 Sep 2015, 01:00, edited 3 times in total.
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Re: Did one of the 3 members of a certain team sell atleast 2 [#permalink]

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12 Oct 2015, 04:54
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Expert's post
kanigmat011 wrote:
what does this mean

" No 2 members sold the same number of tickets"

It means that each of the 3 members sold different number of tickets.

Hope it's clear.

OPEN DISCUSSION OF THIS QUESTION IS HERE: did-one-of-the-3-members-of-a-certain-team-sell-at-least-136811.html
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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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22 Nov 2014, 19:14
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vietnammba
We have a, b, and c (the 3 members). Does a or b or c "great than or equal to" 2?
(1) a+b+c = 6
Possible situations:
a=0, b=0, c=6
a=1, b=1, c=4
a=2, b=2, c=2
a=3, b=3, c=0
...
...
...
--> every situation must have at least a or b or c "equal to or greater than" 2.
--> sufficient

(2) we have: a, b and c must be different from each other:
a=0, b=1, c=2
a=1, b=2, c=0
a=2, b=1, c=0
-->so many situations, but always: a or b or c must be at least 2
-->sufficient

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

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23 Nov 2014, 05:56
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vinhnhat88 wrote:
vietnammba
We have a, b, and c (the 3 members). Does a or b or c "great than or equal to" 2?
(1) a+b+c = 6
Possible situations:
a=0, b=0, c=6
a=1, b=1, c=4
a=2, b=2, c=2
a=3, b=3, c=0
...
...
...
--> every situation must have at least a or b or c "equal to or greater than" 2.
--> sufficient

(2) we have: a, b and c must be different from each other:
a=0, b=1, c=2
a=1, b=2, c=0
a=2, b=1, c=0
-->so many situations, but always: a or b or c must be at least 2
-->sufficient

Thanks, i figured it out last night. I focused on the fact that there might be people selling zero ticket and forgot the fact that if so then the other person has to sell more in order for 3 to sell 6 in total.
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Re: DS -gmatprep1 -- raffle tickets [#permalink]

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11 Mar 2009, 20:08
ugimba wrote:
Did one of the 3 members of a certain team sell atleast 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. it could be that 1 member sold all 6 tickets.
insuffic.

2. any way you slice it, at least 1 member will have sold at least 2 tickets, e.g.

pers1-0 pers2-1 pers3-5
pers1-1 pers2-2 pers3-3
etc.
suffic.

B.
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Re: DS -gmatprep1 -- raffle tickets [#permalink]

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11 Mar 2009, 20:33
peraspera wrote:
ugimba wrote:
Did one of the 3 members of a certain team sell atleast 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. it could be that 1 member sold all 6 tickets.
insuffic.

2. any way you slice it, at least 1 member will have sold at least 2 tickets, e.g.

pers1-0 pers2-1 pers3-5
pers1-1 pers2-2 pers3-3
etc.
suffic.

B.

correcting myself - read the 1) wrong. It's clear from 1) that at least 1 member sold at least 2 tickets.
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Re: DS -gmatprep1 -- raffle tickets [#permalink]

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12 Mar 2009, 06:41
tkarthi4u wrote:
Given:

stmt 1:

3 members sold a total of 6 raffel tickets.
on a average each should sell 2 tickets.
So it can be (2,2,2);(1,2,3);(4,1,1).
So one of the 3 members will definetly sell atleast 2 raffel tickets.
Therefore sufficient .

stmt2 :
No two members sold the same number of raffel tickets.
giving the lowest possible value ( 0,1,2);(1,2,3). Therefore sufficient.

Ans :D.

tkarthi4u , Thank you. Yes OA is D.

your take on second case is very clear. that is where I was confused and picked wrong answer.

+1 to ya.
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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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04 Aug 2012, 10:03
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.

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

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06 Mar 2013, 06:28
ugimba wrote:
Did one of the 3 members of a certain team sell atleast 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.

From F.S 1, we have the total no of raffles being sold as 6. The average no of raffles sold per person would be 6/3 = 2. Thus, any combination between these three people will end up with one person getting more than 2 or at-least 2 raffles. For example, (2,2,2);(0,4,2);(1,1,4) etc. Sufficient.

From F.S 2, we have the no of tickets sold by each is different in value. Assuming that all three of them sold 0 tickets is thus not possible. If one person sold zero tickets, the second person will have to sell 1 or any no. more than that. Similarly, for the third person. Thus, one of the member would have atleast sold atleast 2 raffle tickets. Sufficient.

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

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04 Sep 2013, 12:25
Rax 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 tickets yesterday
(2) No 2 members sold the same number of tickets

A. Statement A alone is sufficient, but Statement B alone is not sufficient
B. Statement B alone is sufficient, but Statement A alone is not sufficient
C. Both statements together are sufficient, but neither alone is sufficient.
D. Each statement alone is sufficient.
E. (1) and (2) together are not sufficient.

Option D is correct answer, but my pick is B.
Any takers?

In each case which is possible, one of the members would sell 2 at least or more. But need to read stems very carefully.
My mistake, picked the first one as sufficient, even did not go through second one in details.
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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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06 Sep 2013, 00:55
Rax 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 tickets yesterday
(2) No 2 members sold the same number of tickets

LOL...this is in the wrong section buddy.

My guess would be D though.

(1) If the three sold a total of 6, it could be any combination of 1,3,2 or 2,2,2 or 0,0,6. Either way, someone sold more than 2. AD
(2) If no 2 members sold the same, well, at the very least you can have 0,1,2 which satisfies.
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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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07 Dec 2014, 10:58
nusmavrik wrote:
1. Sufficient.

Cases : (0,0,6), (0,1,5),(0,2,4),(2,2,2),(1,2,3) etc All add upto 6. So one of the member sold atleast 2 tickets.

2. Sufficient.

Lets look at the min number of tickets that can be sold (when all the three are unequal)

M1 0
M2 1
M3 2

M3 sold atleast 2 tickets.

Hence D.

BUt in the second statement there is noway mentioned that total ticket sold is 6 ??
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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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07 Dec 2014, 23:02
surbhii wrote:
BUt in the second statement there is noway mentioned that total ticket sold is 6 ??

Yes, but with second statement, the boundaries that we have are:

i) 3 members of the team sell tickets
ii) no 2 members sold the same number of tickets.

Any which way you look at it, since there are no way that all the 3 members could have sold less than 2 tickets. For example the combinations could be (0,1,2), (0,1,3), (0,1,5),(3,4,5) or whatever; but it cannot be (0,1,0), (0,0,0), (0,1,1) etc. because no 2 members sold the same number of tickets.
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Re: Did one of the 3 members of a certain team sell at least 2 [#permalink]

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12 Oct 2015, 04:45
what does this mean

" No 2 members sold the same number of tickets"
Re: Did one of the 3 members of a certain team sell at least 2   [#permalink] 12 Oct 2015, 04:45
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