Hi LUANDATO,

We're told that in a certain law firm, Mr. Jones schedules meetings every 15 minutes, Ms. Sollenberg schedules meetings every 20 minutes, and Mrs. Cho schedules meetings every 40 minutes. All three schedule meetings for 9:00 am, take no breaks between scheduled meetings for the remainder of the day and none of the three will begin a meeting AFTER 5:00 pm. We're asked for the number of times - INCLUDING 9:00 am - that all three will have a meeting beginning at the exact same time. While this question is wordy, it has a number of built-in shortcuts that you can use to avoid doing lots of 'busy work.'

To start, Ms. Sollenberg schedules meetings every 20 minutes and Mrs. Cho schedules meetings every 40 minutes. Since 20 divides evenly into 40, this means that we don't have to think about Ms. Sollenberg's meetings at all; we know that when Mrs. Cho has a meeting, Ms. Sollenberg will ALSO have a meeting. Thus, we really just have to compare Mr. Jones' schedule with Mrs. Cho's schedule.

Mr. Jones has meeting every 15 minutes, meaning.... 9:00, 9:15, 9:30, 9:45, 10:00, 10:15, 10:30, 10:45, 11:00, etc.
Mrs. Cho has meeting every 40 minutes, meaning.... 9:00, 9:40, 10:20, 11:00

Notice how the only 'overlap' occurs every 2 hours (beginning at 9:00). Thus, the times when all 3 people have meetings beginning at the same time are:
9:00, 11:00, 1:00, 3:00 and 5:00 --> 5 times

Final Answer: D

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

BTGmoderatorLU wrote:In a certain law firm, Mr. Jones schedules meetings every 15 minutes, Ms. Sollenberg schedules meetings every 20 minutes, and Mrs. Cho schedules meetings every 40 minutes. All three schedule meetings for 9:00 am and take no breaks between scheduled meetings for the remainder of the day. If none of the three will begin a meeting after 5:00 pm, how many times including 9:00 am will all three have a meeting beginning at the exact same time?

A. 2
B. 3
C. 4
D. 5
E. 6
.

The LCM of 15, 20, and 40 is 120. Since 120 minutes = 2 hours, every 2 hours the three meetings occur at the same time. That is the three lawyers' meetings occur at the same time at 9 am, 11 am, 1 pm, 3 pm and 5 pm, for a total of 5 times.

Answer: D