ziyuenlau wrote: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

Source : Veritas Prep
OA : C

Hi ziyuenlau,

Both the clocks will show the same time again when their difference of time is 12 hours.

Since one is gaining and the other is losing time, in every 1 hour, the relative difference is 45 seconds (30 + 15)

Since 45 seconds the relative difference in 1 hour, the 12 hours difference is achieved in (12*60*60) / 45 = 960 hours = 960/24 days = 40 days.

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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Hi ziyuenlau,

This question can be solved by TESTing THE ANSWERS.

The north clock 'loses' 30 seconds per hour (or 1/2 minute per hour) and the south clock 'gains' 15 seconds per hour (or 1/4 minute per hour). Both clocks begin at 12:00. We're asked how long it will be before they show the exact same time. Since the answer choices are all in DAYS, we can do a bit of 'upfront' work and convert these rates....

North clock = loses 24(1/2) = 12 minutes per day = 1/5 of an hour per day
South clock = gains 24(1/4) = 6 minutes per day = 1/10 of an hour per day

Since the fractions (1/5 and 1/10) can both be eliminated if we multiply by a multiple of 10, let's start with the one answer that is a multiple of 10...

Let's TEST Answer A: 40 days

In 40 days...
The north clock loses 40(1/5) = 8 hours - so instead of 12:00, it's... 12:00 - 8 hours = 4:00
The south clock gains 40(1/10) = 4 hours - so instead of 12:00, it's... 12:00 + 4 hours = 4:00
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: C

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

hazelnut01 wrote: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