The organizers of a conference offered a certain number of s

[BTGmoderatorDC]

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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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

[swerve]

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.

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

[Scott@TargetTestPrep]

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

We can let n = the number of seminars and create the equation:

18n = 15(n - 4) + 93

18n = 15n - 60 + 93

3n = 33

n = 11

Answer: B