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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
The organizers of a conference offered a certain number of simultaneou
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16 Nov 2021, 08:29
16 Nov 2021, 08:29
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Question Stats:
66% (01:33) correct
33% (02:28) wrong based on 3 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
(A) 10
(B) 11
(C) 15
(D) 20
(E) 26
Re: The organizers of a conference offered a certain number of simultaneou
[#permalink]
16 Nov 2021, 22:46
16 Nov 2021, 22:46
1
Total number of seminars = \(n\)
The organizers initially accounted for 18 attendees for each seminar.
Total number of attendees = 18n
But space limitations allowed only 15 attendees per seminar. The rearrangement resulted in 4 seminars that were together attended by at least 93 attendees.
Which means \((n-4)\) seminars had 15 attendees each.
The final equation can be formed as follows -
(Total number of attendees in \((n-4)\) seminars) + Total number of attendees in remaining 4 seminars = Total number of attendees in \(n\) seminars where space limitations were not taken into consideration
\((n-4)*15 + 93 = n*18\)
\(15n - 60 + 93 = 18n\)
\(18n - 15n = 93 - 60\)
\(3n = 33\)
\(n = \textbf{11}\)
Hence, Answer is B
The organizers initially accounted for 18 attendees for each seminar.
Total number of attendees = 18n
But space limitations allowed only 15 attendees per seminar. The rearrangement resulted in 4 seminars that were together attended by at least 93 attendees.
Which means \((n-4)\) seminars had 15 attendees each.
The final equation can be formed as follows -
(Total number of attendees in \((n-4)\) seminars) + Total number of attendees in remaining 4 seminars = Total number of attendees in \(n\) seminars where space limitations were not taken into consideration
\((n-4)*15 + 93 = n*18\)
\(15n - 60 + 93 = 18n\)
\(18n - 15n = 93 - 60\)
\(3n = 33\)
\(n = \textbf{11}\)
Hence, Answer is B
gmatclubot
Re: The organizers of a conference offered a certain number of simultaneou [#permalink]
16 Nov 2021, 22:46
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