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

BTGmoderatorDC wrote: ↑

Mon Apr 19, 2021 3:13 pm

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

Algebraic approach,

# of seminar\(= s\)
# of seminar with space limitations\(= x\)

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

Total number of INTENDED attendees\(= 18\cdot s\)
Total number of attendees in seminar with limitations\(= 15\cdot x\)

Number of remaining attendees \(=\) intended attendees \(-\) attendees with limitations \(\geq 93\)

\(18s-15x \geq 93 \quad (2)\)

Solving \((1)\) and \((2)\)
\(x=7\)
\(s=4+7\)
\(s=11\quad\Longrightarrow\quad\)B