The organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar

[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

[jbryant62]

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

If you aren't good at setting up equations, just try the answer choices. Since they originally wanted 18 members to be equally divided amongst the seminars, we know the total members are a multiple of 18. Lets check using the answers.

A. if there are 10 seminars, and 4 were attended by 93, then there are 6 seminars attended by 15 each.

6*15=90. 90+93=183. 183/18= is not an integer. not correct.

B. if there are 11 seminars, and again 4 are attended by 93, this leaves 7 seminars attended by 15 each.

7*15=105. 105+93=198 . 198/18=11. Correct.

answer B.

[swerve]

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

Let \(T =\) total number of attendees
Let \(S =\) total number of seminars

Initial Plan: \(T = 18S\)
Actual: \(T = 15(S-4) + 93\)

So we have 2 equations and 2 unknowns.

\(18S = 15S - 60 + 93\)
\(3S = 33\)
\(S =11\)

Hence, the correct answer is B