A conference room has two analog (12-hour format) clocks,

Expert replies

Previous Topic Next Topic

AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Wed Sep 19, 2018 4:41 am

Timer

00:00

Answers

Stats

Difficulty—

Veritas Prep

A conference room has two analog (12-hour format) clocks, one on the north wall and one on the south wall. The clock on the north wall loses 30 seconds per hour, and the clock on the south wall gains 15 seconds per hour. If the clocks begin displaying the same time, after how long will they next display the same time again?

A. 32 days
B. 36 days
C. 40 days
D. 44 days
E. 48 days

OA C.

Like this post

Source: Beat The GMAT — Problem Solving | Wed Sep 19, 2018 4:41 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sun Sep 23, 2018 8:50 am

The clock on the north wall loses twice as much time as the clock on the south wall gains,
Assuming that both clock starts from 12 o'clock,
The next time they will display the same time is 4 o'clock because by that time the clock on the north wall would have lost 8 hours and the clock on the south wall would have gained 4 hours.

South Wall Clock=
4 hours to seconds = 60 * 60 * 4 = 14,4000 seconds and the clock gains 15 seconds per hour. For it to get to 4 o'clock at the same time with the north clock on the north wall=
15 seconds = 1 hour
14,4000 seconds = x (cross match)
$$x\ =\ \frac{\left(14,400\right)}{15\ }=\ 960\ hours.$$
24 hours = 1 day
960 hours = x
$$x\ =\ \frac{960}{24}=\ 40\ days.$$

North Wall Clock=
8 hours to seconds = 60 * 60 * 8 = 28, 800s and this clock loses 30 seconds per hour for it to get to 4 o'clock at the same time with the clock on the south wall.
30 secounds = 1 hour
28,800 seconds = x
$$x\ =\ \frac{28800}{30}=960\ hours.$$
24 hours = 1 day
$$960\ hours=\ \frac{960}{24}=40\ days.$$
In either clock, the number of days needed = 40
Option C is CORRECT.

Like this post

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

A conference room has two analog (12-hour format) clocks,

by fskilnik@GMATH » Sun Sep 23, 2018 11:26 am

AAPL wrote:Veritas Prep

A conference room has two analog (12-hour format) clocks, one on the north wall and one on the south wall. The clock on the north wall loses 30 seconds per hour, and the clock on the south wall gains 15 seconds per hour. If the clocks begin displaying the same time, after how long will they next display the same time again?

A. 32 days
B. 36 days
C. 40 days
D. 44 days
E. 48 days

This is an excellent example of a problem in which "blending" two of our most powerful techniques solves the exercise immediately (in just one line)!
Techniques: Relative Velocity AND Units Control
\[\left\{ \begin{gathered}
{\text{North}}:\,\,\frac{{ - 30\,\,{\text{s}}}}{{1\,\,{\text{h}}}} \hfill \\
{\text{South}}:\,\,\frac{{ + 15\,\,{\text{s}}}}{{1\,\,{\text{h}}}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\, \sim \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( * \right)\,\,\,\left\{ \begin{gathered}
{\text{North}}:\,\,{\text{regular}}\,\,{\text{clock}} \hfill \\
{\text{South}}:\,\,\frac{{ + 45\,\,{\text{s}}}}{{1\,\,{\text{h}}}} \hfill \\
\end{gathered} \right.\]
\[?\,\,{\text{in}}\,\,\left( * \right)\,\,:\,\,\, + 12{\text{h}}\,\,\,\,{\text{in}}\,\,\,{\text{?}}\,\,{\text{h}}\]

Once DATA and FOCUS were structurally presented, letÂ´s connect them! (This is our methodÂ´s "backbone".)

\[?\,\,\,\, = \,\,\,\, + {\text{12h}}\,\,\,\left( {\frac{{60 \cdot 60\,\,\,{\text{s}}}}{{1\,\,{\text{h}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\left( {\frac{{1\,\,{\text{h}}}}{{ + 45\,\,\,{\text{s}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\,\left( {\frac{{1\,\,{\text{day}}}}{{24\,\,{\text{h}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\,\, = \,\,\,\,\,\frac{{12 \cdot 60 \cdot 60}}{{45 \cdot 24}} = 40\,\,{\text{days}}\]
Obs.: arrows indicate licit converters.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Sep 23, 2018 3:45 pm

AAPL wrote:Veritas Prep

A conference room has two analog (12-hour format) clocks, one on the north wall and one on the south wall. The clock on the north wall loses 30 seconds per hour, and the clock on the south wall gains 15 seconds per hour. If the clocks begin displaying the same time, after how long will they next display the same time again?

A. 32 days
B. 36 days
C. 40 days
D. 44 days
E. 48 days

We can see that the clock on the north wall loses twice as much time as the clock on the south wall gains. We can assume the time that both clocks display is 12 o'clock, i.e., the hour hand is on the number 12 on both clocks. The next time they will display the same time is 4 o'clock, since the clock on the south wall gains 4 hours and the clock on the north wall loses 8 hours.

From the south clock point of view:

Since 4 hours = 4 x 3600 = 14400 seconds and the clock on the south wall gains 15 seconds per hour, it needs 14400/15 = 960 hours or 40 days to strike 4 o'clock as the clock on the north wall strikes the same time.

Or, from the north clock point of view:

Since 8 hours = 8 x 3600 = 28800 seconds and the clock on the north wall loses 30 seconds per hour, it needs 28800/30 = 960 hours or 40 days to strike 4 o'clock as the clock on the south wall strikes the same time.

In either case, the number of days needed is 40.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Sep 23, 2018 7:27 pm

Hi All,

We're told that a conference room has two analog (12-hour format) clocks, one on the north wall and one on the south wall; the clock on the north wall LOSES 30 seconds per HOUR, and the clock on the south wall GAINS 15 seconds per HOUR. We're asked, if the clocks begin displaying the SAME time, after how long will they next display the SAME time again. This question can be approached in a number of different way, but you can take advantage of the 'format' of the answer choices to do some minimal math to find the correct answer.

Since all five answers are in 'days', we can think of all of these calculations in terms of how the rates are calculated per day.
The North clock loses 30 seconds/hour; with 24 hours/day, that would be 12 minutes LOST per DAY.
The South clock gains 15 seconds/hour; with 24 hours/day, that would be 6 minutes GAINED per DAY.

There are 60 minutes/hour, so to make these calculations a little easier to think about, I'm going to think in terms of hours instead of minutes:
After 5 days....
The North clock will have LOST (12 minutes/day)(5 days) = 60 minutes in 5 days = 1 hour LOST every 5 days
The South clock will have GAINED (6 minutes/day)(5 days) = 30 minutes in 5 days = 1/2 hour GAINED every 5 days

Thus, every multiple of 5 days will give us a relatively nice fraction (either 1 or 1/2). Looking at the answer choices, there's only one answer that's a multiple of 5....
IN 40 DAYS.....
The North clock will have LOST (1 hour/5 days)(40 days) = 8 hours LOST every 40 days
The South clock will have GAINED (1/2 hour/5 days)(40 days) = 4 hours GAINED every 40 days.
On a 12-hour clock face, 8 hours lost combined with 4 hours gained would lead to the exact SAME time, so this MUST be the answer.

Final Answer: C

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

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review