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# At a business school conference with 100 attendees, are ther

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Re: At a business school conference with 100 attendees, are ther [#permalink]
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enigma123 wrote:
At a business school conference with 100 attendees, are there any students of the same age (rounded to the nearest year) who attend the same school?
(1) The range of ages of the participants is 22 to 30, inclusive
(2) Participants represent 10 business schools.

For me its clearcut A. Can someone please let me know if you think it not correct? OA is not provided unfortunately.

I believe the answer should be C.

S1: Only the range of age is given. But there may be 100 different or only 1/2 colleges. In that case the answer in insufficient.
S1: Only #of B schools are given.We don't have the range of age. Insufficient

S1+S2 = we have all the data. Sufficient. hence IMO D.
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Re: At a business school conference with 100 attendees, are ther [#permalink]
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imo C.

Stmt 1 does not tell you how many schools there are. So all though you have a range of 9 years for 100 attendees, there could be 100 schools.

Stmt 2 is not enough for the same reason. We know that there are 10 schools but the age range could be anything.

Stmt 1 & 2: suff
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Re: At a business school conference with 100 attendees, are ther [#permalink]
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very hard.

at one school, the maximum student diferent at age is 9 (there are 9 ages).

we have 10 schools,so, the number of students with different ages at different schools is 90

some school must have more than 9 students. those schools must contain student at the same age
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Re: At a business school conference with 100 attendees, are ther [#permalink]
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Statement 1: Not sufficient
It doesn't mention the number of schools which had their students participate in the conference.

Statement 2: Not sufficient
We don't know the range of the age of the students attending the conference. There can be only one student from the participating colleges or 100 students from the same college.

Together: Sufficient
Range: 22-30 = 9 age group
Number of participating schools: 10
Total number of students attending the conference: 100
Min number of students from each age group: 9*10 = 90
Therefore, there has to be at least one repeatation (actually 10 repeatation) in the age group.

Note: Statement 1 can be mistaken to be the answer if we don't read the last few words of the question ("who attend the same school"). Happened with me :D

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Re: At a business school conference with 100 attendees, are ther [#permalink]
hard one.

look at both 1 and 2.

there are at least 10 student in one business school
there are at most 9 ages. so if 10 student are different most, at least 2 student have the same age.

C
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Re: At a business school conference with 100 attendees, are ther [#permalink]
(rounded to the nearest year)
what is the importance of this part in the question?
I thought like 21 years 6 months would become 22 years...
so we have range from 21 years to 30 years
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Re: At a business school conference with 100 attendees, are ther [#permalink]
r19 wrote:
(rounded to the nearest year)
what is the importance of this part in the question?
I thought like 21 years 6 months would become 22 years...
so we have range from 21 years to 30 years

You are given that range of ages is 22 to 30. So you do not have a 21 year (after rounding) old. So there is no one whose age is 21 years and 3 months or 20 years and 8 months etc. You might have a 21 year 7 months old (something that will get rounded to 22 years).
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Re: At a business school conference with 100 attendees, are ther [#permalink]
100 attendees.
A) Maybe attendees are all from different schools. or maybe same Insufficient
B) on average, 10 attendees per school. there age can be 21,22...30 or 21,21,...21
Insufficient

A&B) range=22 to 30: 22,23...30 (total 9 ages..)
also 10 business schools. therefore atleast one school will have more than 9 attendees. otherwise total will be only 90 max. Let that school be A.
Now A has 10 students and we have only 9 different ages. Thus atleast 2 students will have same age. Sufficient
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Re: At a business school conference with 100 attendees, are ther [#permalink]
enigma123 wrote:
At a business school conference with 100 attendees, are there any students of the same age (rounded to the nearest year) who attend the same school?

(1) The range of ages of the participants is 22 to 30, inclusive
(2) Participants represent 10 business schools.

For me its clearcut A. Can someone please let me know if you think it not correct? OA is not provided unfortunately.

without using pen and paper:

Stmt 1: we can't do anything with a range without knowing the number of schools the students belong to. Not sufficient
Stmt 2: again, without information of ages/range of age we cannot solve this.

combining 1 & 2: we know that there are 10 B Schools and 9 (from 22-30 exclusive) age groups, therefore some have to belong to the same school, i.e, the least number of age repetitions within the same school is 1 (can be more but we don't need that to answer the question)

therefore, C stands.
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Re: At a business school conference with 100 attendees, are ther [#permalink]
Can we say that we need to have minimum 12 business schools to get 22-30 age group from different schools?
9*11= 99. Hence 12 different schools.
Since option B mentions that there are only 10 business schools, hence there we be students of the same age and same business schools.
Re: At a business school conference with 100 attendees, are ther [#permalink]
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