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# Of the 66 people in a certain auditorium, at most 6 people

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Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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09 Jun 2010, 11:59
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60% (01:25) correct 40% (01:43) wrong based on 865 sessions

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Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January?

(1) More of the people in the auditorium have their birthday in February than in March.
(2) Five of the people in the auditorium have their birthday in March.

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09 Jun 2010, 13:33
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mojorising800 wrote:
Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January?

(1) More of the people in the auditorium have their birthday in February than in March.
(2) Five of the people in the auditorium have their birthday in March.

Basically the question is whether we can distribute 66 birthdays between 12 moths so that January to get 0.

(1) Let 10 months (except March and January) have 6 birthdays each (maximum possible) --> 6*10=60. As in March there was less birthdays than in February than maximum possible for March is 5 --> total 60+5=65, so even for the worst case scenario (maximum for other months) still 1 birthday (66-65=1) is left for January. Sufficient.

(2) Again: let 10 months have 6 birthdays each (maximum possible) --> 6*10=60 + 5 birthdays in March = 65. The same here: even for the worst case scenario (maximum for other months) still 1 birthday (66-65=1) is left for January. Sufficient.

Hope it helps.
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Re: Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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31 May 2013, 09:21
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Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January?

Pre-thinking: in the worst case scenario there are 11 months each with 6 people => 1 month out with 0.
We start from here because if we do NOT assume this, then all months have at least one person, and the question does not make sense.

(1) More of the people in the auditorium have their birthday in February than in March.
This could mean two things:
1) The month "out" is March (0 people), in this case January is one of the month with 6 people.
2) March and February cannot both have 6 people => in the worst case March has 5 people, and all months have at least one person now.
Both cases are sufficient

(2) Five of the people in the auditorium have their birthday in March.
So we take the 6 people of March, take one out and assign it to to a new month (because all the others have 6 already).
In this scenario all months have at least one person, sufficient

Hope this makes sense
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09 Jun 2010, 12:09
mojorising800 wrote:
Of the 66 people in a certain auditorium, at most
6 people have their birthdays in any one given month.
Does at least one person in the auditorium have a
birthday in January?
(1) More of the people in the auditorium have their
birthday in February than in March.
(2) Five of the people in the auditorium have their
birthday in March.

IMO D

Given that no of people who have birthdays in month is at most 6. So for 66 people, one of the possibilities is to have 6 people place is every month leaving out one of the months with no birthdays.

A - SUFFICIENT (more birthdays in Feb than in March means that there should at least 1 birthday in Jan even if Jan was left out initially.
B - SUFFICIENT (Same reason as A)
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Re: Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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31 May 2013, 05:43
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
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Re: Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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06 Jan 2014, 11:42
1
Apologies for flaring up an old topic.

Given both the question and the solution come from OG, there is certainly no conflict over the answer and its explanation. However, I find the answer incorrect. My reasoning for the same is as follows.

1) Agreed, this is sufficient
2) The statement reads as "Five of the people in the auditorium have birthdays in March". The statement to me reads as 5 people from the auditorium have birthdays in March, however it does not say these are the only 5 people whose birthday falls in March. Logically "only" is a required qualifier for the reader to conclude that there are only 5 such people. I don't think statement 2 will be incorrect if there are 6 people who have their birthdays in March. Therefore, the correct answer of this question should be (A).

I understand at the end of the day whatever OG mentions will be construed as correct answer, but I feel my logic is correct. I solicit your views on this.
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Re: Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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07 Jan 2014, 00:02
2
ankurdubey wrote:
Apologies for flaring up an old topic.

Given both the question and the solution come from OG, there is certainly no conflict over the answer and its explanation. However, I find the answer incorrect. My reasoning for the same is as follows.

1) Agreed, this is sufficient
2) The statement reads as "Five of the people in the auditorium have birthdays in March". The statement to me reads as 5 people from the auditorium have birthdays in March, however it does not say these are the only 5 people whose birthday falls in March. Logically "only" is a required qualifier for the reader to conclude that there are only 5 such people. I don't think statement 2 will be incorrect if there are 6 people who have their birthdays in March. Therefore, the correct answer of this question should be (A).

I understand at the end of the day whatever OG mentions will be construed as correct answer, but I feel my logic is correct. I solicit your views on this.

Think about the sets questions you solve regularly.

55 of the 100 people drink tea. Do you take it as 55 drink tea and 45 do not or do you take it as 'at least 55 drink tea'?
When you are given that of the 100 people, 55 drink tea, it means only 55 drink tea.
Similarly, 5 of the people in the auditorium have their birthday in March means only 5 do.
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Re: Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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15 Jan 2014, 03:15
VeritasPrepKarishma wrote:
ankurdubey wrote:
Apologies for flaring up an old topic.

Given both the question and the solution come from OG, there is certainly no conflict over the answer and its explanation. However, I find the answer incorrect. My reasoning for the same is as follows.

1) Agreed, this is sufficient
2) The statement reads as "Five of the people in the auditorium have birthdays in March". The statement to me reads as 5 people from the auditorium have birthdays in March, however it does not say these are the only 5 people whose birthday falls in March. Logically "only" is a required qualifier for the reader to conclude that there are only 5 such people. I don't think statement 2 will be incorrect if there are 6 people who have their birthdays in March. Therefore, the correct answer of this question should be (A).

I understand at the end of the day whatever OG mentions will be construed as correct answer, but I feel my logic is correct. I solicit your views on this.

Think about the sets questions you solve regularly.

55 of the 100 people drink tea. Do you take it as 55 drink tea and 45 do not or do you take it as 'at least 55 drink tea'?
When you are given that of the 100 people, 55 drink tea, it means only 55 drink tea.
Similarly, 5 of the people in the auditorium have their birthday in March means only 5 do.

Thanks VeritasPrepKarishma. While I agree with you, I was stumped by this question from one of the reputed practise tests.

Team A and team B competed in 8 distinct consecutive events. The team winning the nth event was given n points, there were no other teams competing, and there were no ties in any event. Did team A receive more points than team B?

(1) Team A won the seventh and eighth events and at least one other event.

(2) Team B won the third, fourth, and fifth events.

Based on what you noted, I came up with the answer (B) i.e. Statement 2 is sufficient, but the solution given by the prep company is as follows

"Now consider Statement (2). Team B won the third, fourth, and fifth events. For these events team B received 3 + 4 + 5, or 12 points. However, we have no information about which team won the remaining events. If team A won all the other events, then team A received 36 − 12, or 24 points. In this case the answer to the question is YES. However, if team B won all 8 events, then team A received no points while team B received all 36 points, and in this case the answer to the question is NO. Statement (2) is Insufficient, and we can eliminate choice (B)"

As you see, this is exactly what I was contending earlier. Is there any concrete method to tackle such ambiguous questions.
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Re: Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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02 Jul 2016, 04:42
VeritasPrepKarishma wrote:

Given both the question and the solution come from OG, there is certainly no conflict over the answer and its explanation. However, I find the answer incorrect. My reasoning for the same is as follows.

1) Agreed, this is sufficient
2) The statement reads as "Five of the people in the auditorium have birthdays in March". The statement to me reads as 5 people from the auditorium have birthdays in March, however it does not say these are the only 5 people whose birthday falls in March. Logically "only" is a required qualifier for the reader to conclude that there are only 5 such people. I don't think statement 2 will be incorrect if there are 6 people who have their birthdays in March. Therefore, the correct answer of this question should be (A).

I understand at the end of the day whatever OG mentions will be construed as correct answer, but I feel my logic is correct. I solicit your views on this.

Think about the sets questions you solve regularly.

55 of the 100 people drink tea. Do you take it as 55 drink tea and 45 do not or do you take it as 'at least 55 drink tea'?
When you are given that of the 100 people, 55 drink tea, it means only 55 drink tea.
Similarly, 5 of the people in the auditorium have their birthday in March means only 5 do.[/quote]

I do agree with VeritasPrepKarishma

Also considering the example put forward by Ankurdubey :

ankurdubey wrote:

Team A and team B competed in 8 distinct consecutive events. The team winning the nth event was given n points, there were no other teams competing, and there were no ties in any event. Did team A receive more points than team B?

(1) Team A won the seventh and eighth events and at least one other event.

(2) Team B won the third, fourth, and fifth events.

Based on what you noted, I came up with the answer (B) i.e. Statement 2 is sufficient, but the solution given by the prep company is as follows

"Now consider Statement (2). Team B won the third, fourth, and fifth events. For these events team B received 3 + 4 + 5, or 12 points. However, we have no information about which team won the remaining events. If team A won all the other events, then team A received 36 − 12, or 24 points. In this case the answer to the question is YES. However, if team B won all 8 events, then team A received no points while team B received all 36 points, and in this case the answer to the question is NO. Statement (2) is Insufficient, and we can eliminate choice (B)"

As you see, this is exactly what I was contending earlier. Is there any concrete method to tackle such ambiguous questions.
[/quote][/quote]

I am confused with what approach to follow, can any of the experts here suggest how to tackle such questions and come up with a concrete understanding of the question along with the right answer?
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Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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17 Jan 2019, 17:23
ankurdubey wrote:
Apologies for flaring up an old topic.

Given both the question and the solution come from OG, there is certainly no conflict over the answer and its explanation. However, I find the answer incorrect. My reasoning for the same is as follows.

1) Agreed, this is sufficient
2) The statement reads as "Five of the people in the auditorium have birthdays in March". The statement to me reads as 5 people from the auditorium have birthdays in March, however it does not say these are the only 5 people whose birthday falls in March. Logically "only" is a required qualifier for the reader to conclude that there are only 5 such people. I don't think statement 2 will be incorrect if there are 6 people who have their birthdays in March. Therefore, the correct answer of this question should be (A).

I understand at the end of the day whatever OG mentions will be construed as correct answer, but I feel my logic is correct. I solicit your views on this.

I agree with ankurdubey. There was another question in the same Diagnostic Test. It said that a number had prime factors: 2, 3 and 5. But in the answer, they said that it was not sufficient because there was no ONLY word in the context and there could be other prime factors as well. Question #26, Diagnostic Test. What should we believe in?

If I didn't think of the ONLY word missing, I would answer the 56th question correctly. Otherwise, I made a wrong answer
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Re: Of the 66 people in a certain auditorium, at most 6 people  [#permalink]

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28 Jan 2019, 05:58
mojorising800 wrote:
Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January?

(1) More of the people in the auditorium have their birthday in February than in March.
(2) Five of the people in the auditorium have their birthday in March.

$$0\,\, \leqslant \,\,J,F,M, \ldots ,N,D\,\, \leqslant \,\,6\,\,\,\left( * \right)\,\,\,\,\,\,\left( {{\text{ints}}} \right)$$

$$J + F + M + \ldots + N + D = 66\,\,\,\,\,\,\, \Rightarrow \,\,\,{\mu _{{\text{all}}}} = 5.5\,\,\frac{{{\text{birthdays}}}}{{{\text{month}}}}$$

$$?\,\,\,:\,\,\,J\,\,\mathop \geqslant \limits^? \,\,1$$

$$\left( 1 \right)\,\,F > M\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\left\langle {{\text{YES}}} \right\rangle$$

$$\left( {**} \right)\,\,\,J = 0\,\,\,\, \Rightarrow \,\,\,{\mu _{{\text{all}}\, - \,\left\{ J \right\}}} = 6\,\,\frac{{{\text{birthdays}}}}{{{\text{month}}}}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\underline {F = M} = \ldots = N = D = 6\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\underline {{\text{impossible}}}$$

$$\left( 2 \right)\,\,\,M = 5\,\,\,\,\mathop \Rightarrow \limits^{\left( {***} \right)} \,\,\,\left\langle {{\text{YES}}} \right\rangle$$

$$\left( {***} \right)\,\,\,J = 0\,\,\,\, \Rightarrow \,\,\,{\mu _{{\text{all}}\, - \,\left\{ J \right\}}} = 6\,\,\frac{{{\text{birthdays}}}}{{{\text{month}}}}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,F = \underline M = \ldots = N = D = \underline 6 \,\,\,\,\, \Rightarrow \,\,\,\,\,\,\underline {{\text{impossible}}}$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Of the 66 people in a certain auditorium, at most 6 people   [#permalink] 28 Jan 2019, 05:58
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