The organizers of a conference offered a certain number of s

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

The organizers of a conference offered a certain number of s

by BTGmoderatorDC » Tue Feb 05, 2019 4:46 am

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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

OA B

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Tue Feb 05, 2019 4:46 am

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by [email protected] » Tue Feb 05, 2019 10:37 am

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!

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Wed Feb 06, 2019 8:15 am

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.

$$18\cdot 4 = 72$$
$$93 - 72 = 21 \text{ people were from the scheduled seminars.}$$
$$\text{Diving }\frac{21}{18 - 15}, \text{ we get }7 \text{ seminars.} $$
$$7 + 4 = 11 \text{ seminars}$$

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Feb 06, 2019 6:33 pm

BTGmoderatorDC 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?

(A) 10
(B) 11
(C) 15
(D) 20
(E) 26

OA B

Source: GMAT Prep