beat_gmat_09 wrote:A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 15 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
(A) 5:00
(B) 5:34
(C) 5:42
(D) 6:00
(E) 6:24
Source: Manhattan
OA soon.
Let's determine the time displayed on each clock after an actual hour (60 minutes) have passed.
Clock 1 loses 15 minutes every hour. So after 60 minutes have passed, clock 1 displays the passing of 60-15 = 45 minutes.
Clock 2 gains 15 minutes for every 60 minutes displayed on clock 1. Thus, the time displayed on clock 2 is 75/60 = 5/4 the time displayed on clock 1. So after 60 minutes have passed, clock 2 displays the passing of (5/4 * 45) minutes.
Clock 3 loses 20 minutes for every 60 minutes displayed on clock 2. Thus, the time displayed on clock 3 is 40/60 = 2/3 the time displayed on clock 2. So after 60 minutes have passed, clock 3 displays the passing of (2/3 * 5/4 * 45) minutes.
Clock 4 gains 20 minutes for every 60 minutes displayed on clock 3. Thus, the time displayed on clock 4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, clock 4 displays the passing of 4/3 * 2/3 * 5/4 * 45 = 50 minutes.
Thus, clock 4 loses 10 minutes every hour.
In 6 hours, clock 4 will lose 6*10 = 60 minutes = 1 hour.
Since the correct time after 6 hours will be 6pm, clock 4 will show a time of 6-1 = 5pm.
The correct answer is
A.
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