Clocks

[beat_gmat_09]

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.

[neerajkumar1_1]

clock 1 loses 15 mins every hour to real time
while clock 2 gains 15 mins every hour relative to clock 1...

that means clock 2 is showing the real time...

now again,
clock 3 loses 20 mins every hour relative to clock 2, or actual time,
while clock 4 clock 4 gains 20 mins every hour relative to clock 3...

that means clock 4 is showing the actual time..

so after 6 hrs,
time in clock 4 would be 6:00, Pick D

I have solved it by logic, but one can do it with help of relative velocity too...

[beat_gmat_09]

clock 1 loses 15 mins every hour to real time
while clock 2 gains 15 mins every hour relative to clock 1...

that means clock 2 is showing the real time...

now again,
clock 3 loses 20 mins every hour relative to clock 2, or actual time,
while clock 4 clock 4 gains 20 mins every hour relative to clock 3...

that means clock 4 is showing the actual time..

so after 6 hrs,
time in clock 4 would be 6:00, Pick D

I have solved it by logic, but one can do it with help of relative velocity too...

Sorry bro, D is incorrect.

[GMATGuruNY]

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.

[beat_gmat_09]

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.

Thanks Mitch for such a wonderful explanation !

[Scott@TargetTestPrep]

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


OA soon.

Solution:

When it is actually 6:00 pm, Clock #1 will display 4:30pm because this clock loses 15 minutes for each hour, and in six hours, it will lose 6 x 15 = 90 minutes. Notice that we find 4:30 pm if we go back 90 minutes = 1.5 hours from 6:00 pm.

When Clock #1 is displaying 4:30pm (i.e. when Clock #1 moved a total of 4.5 hours), Clock #2 will have gained 4.5 * 15 = 9/2 * 15 = 67.5 minutes relative to Clock #1. Thus, Clock #2 will display 4:30 + 67.5 minutes = 5:30 + 7.5 minutes = 5:37:30.

We see that Clock #2 moved a total of 5 hours + 37.5 minutes = 337.5 minutes. Since Clock #3 loses 20 minutes every hour relative to Clock #2, Clock #3 will have lost (337.5/60) * 20 = 337.5/3 = 112.5 minutes. Thus, Clock #3 will have moved 337.5 - 112.5 = 225 minutes = 3 hours 45 minutes. Thus, it will display 12 pm + 3 hours 45 minutes = 3:45 pm.

Finally, when Clock #3 moved 3 hours 45 minutes, Clock #4 will have gained 3 hr 45 min * 20 = 15/4 * 20 = 75 minutes relative to Clock #3. Thus, Clock #4 will display 3:45 pm + 75 minutes = 5:00 pm.

Answer: A