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The organizers of a conference offered a certain number

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The organizers of a conference offered a certain number  [#permalink]

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New post 01 May 2017, 01:59
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Question Stats:

64% (02:23) correct 36% (02:43) wrong based on 183 sessions

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The organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conference attendees. However, space limitations allowed only up to 15 conference attendees to participate in each of a number of the seminars, leaving 4 remaining seminars that together would be attended by at least 93 conference attendees. How many seminars were there?

(A) 10
(B) 11
(C) 15
(D) 20
(E) 26
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Re: The organizers of a conference offered a certain number  [#permalink]

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New post 01 May 2017, 04:34
paidlukkhha wrote:
The organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conference attendees. However, space limitations allowed only up to 15 conference attendees to participate in each of a number of the seminars, leaving 4 remaining seminars that together would be attended by at least 93 conference attendees. How many seminars were there?


10
11
15
20
26


18x > 15(x-4)+93

i.e. 3x > 33
i.e. x > 11

x min = 11

Answer option B
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Re: The organizers of a conference offered a certain number  [#permalink]

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New post 14 May 2017, 05:19
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Four Seminars were attended by 93 people. Since the intention was to accommodate 18 per seminar. The possible number of seminars should be a multiple of 18. Also, the organizers were able to accommodate only 15 per seminar. Those who could not be accommodated in these seminars, were part of the 93 people who were adjusted for 4 seminars.

18 * 4 = 72

93 - 72 = 21 people were from the schedule seminars.

Diving 21 / (18 - 15), we get 7 seminars.

7 + 4 = 11 seminars
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Re: The organizers of a conference offered a certain number  [#permalink]

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New post 14 May 2017, 22:04
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paidlukkhha wrote:
The organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conference attendees. However, space limitations allowed only up to 15 conference attendees to participate in each of a number of the seminars, leaving 4 remaining seminars that together would be attended by at least 93 conference attendees. How many seminars were there?


10
11
15
20
26


Number of attendees per Seminar as per original plan = 18
Due to space limitations, max number of attendees = 15
Also, there are 4 seminars without any seating constraints and have total attendees of at least = 93
As per original plan, these 4 seminars would have had = 18*4 = 72
So , there are 21 extra attendees in these 4 seminars without space limitations
Therefore, number of seminars with seating limitation = (93-72)/3 = 7
Total number of seminars = 4+7 =11
Answer B
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Re: The organizers of a conference offered a certain number  [#permalink]

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New post 30 Aug 2018, 22:02
Algebraic approach-

# of seminar= s
# of seminar with space limitations= x

Now remaining seminar without limitation:
s-x = 4 ..... (1)

Total number of INTENDED attendees= 18*s
Total number of attendees in seminar with limitations= 15*X

Number of remaining attendees = intended attendees-attendees with limitations >=93

18s-15x >=93 .....(2)

Solving (1) and (2)
X=7
s=4+7
s=11.... option B

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Re: The organizers of a conference offered a certain number  [#permalink]

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New post 05 Feb 2019, 22:33
Hi All,

We're told that the organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conference attendees. However, space limitations allowed only up to 15 conference attendees to participate in each of a number of the seminars, leaving 4 remaining seminars that together would be attended by at least 93 conference attendees. We're asked for the total number of seminars that were planned. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

Let's TEST Answer D: 20 seminars
With an expectation of 18 attendees/seminar, (18)(20) = 360 attendees.
16 seminars can hold only 15 attendees each, accounting for (16)(15) = 240 attendees.
360 - 240 = 120 additional attendees, but the remaining 4 seminars are only expected to hold 93 attendees.
In this situation, we have too many attendees, so this number is TOO BIG. We need fewer attendees, thus we need fewer seminars

Let's TEST Answer B: 11 seminars
With an expectation of 18 attendees/seminar, (18)(11) = 198 attendees.
7 seminars can hold only 15 attendees each, accounting for (7)(15) = 105 attendees.
198 - 105 = 93 additional attendees. This is an exact match for what we were told, so this must be the answer!

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Re: The organizers of a conference offered a certain number   [#permalink] 05 Feb 2019, 22:33
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