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Mark owns four low quality watches. Watch1 loses 15 minutes

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Mark owns four low quality watches. Watch1 loses 15 minutes

by swerve » Fri May 11, 2018 9:38 am

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Mark owns four low-quality watches. Watch1 loses 15 minutes every hour. Watch2 gains 15 minutes every hour relative to watch1 (that is, as watch1 moves from 12:00 to 1:00, watch2 moves from 12:00 to 1:15). Watch3 loses 20 minutes every hour relative to watch2. Finally, watch4 gains 20 minutes every hour relative to watch3. If Mark resets all four watches to the correct time at 12 noon, what time will watch4 show at 12 midnight that day?

A. 10:00
B. 10:34
C. 11:02
D. 11:48
E. 12:20

The OA is A.

Let h be elapsed actual hours

W1 will show = h - h/4 = 3h/4 hours
W2 will show = 3h/4 + 3h/4/4 = 15h/16 hours
W3 will show = -15h/16 - 15h/16/3 = 5h/8 hours
W4 will show = 5h/8 + 5h/8/3 = 5h/6 hours

H = 12 hours so W4 would show 5*12/6 = 10 hours from zero. Option A.
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by deloitte247 » Sat May 19, 2018 1:51 pm
Relative speed
Let the speed of a correct watch =5
Watch 1 loses 15 minutes every hour (it covers on $$\frac{3}{4}of\ one\ hour$$ )
speed of watch 1= $$\left(\frac{3}{4}\right)\cdot s$$

Watch 2 gains 15 minutes every hour (this is relative to watch 1 i.e as watch 1 moves from 12:00 to 1:00, watch 2 moves from 12:00 to 1:15)
speed of watch 2 is relative to speed of watch 1 and is 5/4 times greater than speed of watch 1
speed of watch 2 = $$\left(\frac{5}{4}\cdot\frac{3}{4}\right)\cdot5$$
= $$\left(\frac{15}{16}\right)\cdot5$$

watch 3 loses 20 minutes every hour making the speed to 2/3 of the speed of watch 2
speed of watch 3= $$\left(\frac{2}{3}\cdot\frac{15}{16}\right)\cdot5\ =\ \left(\frac{5}{8}\right)\cdot5$$

watch 4 gains 20 minutes every hour relative to watch 3 i.e 4/3 times the speed of watch 3.
speed of watch 4 = $$\left(\frac{4}{3}\cdot\frac{5}{8}\right)\cdot5$$
$$\left(\frac{5}{6}\right)\cdot5$$
Therefore, if a correct watch shows that 12 hours has passed (from 12 noon to mid night)
watch 4 speed will show that $$\frac{5}{6}\cdot5$$
note s = 12 hours of correct watch
$$\frac{5}{6}\cdot12$$
= 5 * 2 = 10 hours
watch 4 will show that 10 hours has passed and will show the time as 10: 00
Option A is the correct answer.
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by Scott@TargetTestPrep » Tue May 22, 2018 5:14 pm
swerve wrote:Mark owns four low-quality watches. Watch1 loses 15 minutes every hour. Watch2 gains 15 minutes every hour relative to watch1 (that is, as watch1 moves from 12:00 to 1:00, watch2 moves from 12:00 to 1:15). Watch3 loses 20 minutes every hour relative to watch2. Finally, watch4 gains 20 minutes every hour relative to watch3. If Mark resets all four watches to the correct time at 12 noon, what time will watch4 show at 12 midnight that day?

A. 10:00
B. 10:34
C. 11:02
D. 11:48
E. 12:20
We are given that all four watches are reset to the correct time at 12 noon. Since watch 1 loses 15 minutes every hour, let's pit the correct time against watch 1's time (i.e., the time shown on watch 1):

Correct time -------Watch 1's time
1:00 pm ------- 12:45 pm
2:00 pm ------- 1:30 pm
3:00 pm ------- 2:15 pm
4:00 pm ------- 3:00 pm

We see that when the correct time is 4:00 pm, watch 1's time is 3:00 pm. Now let's see watch 2's time. Since watch 2 gains 15 minutes every hour relative to watch 1, then in 3 hours, it will gain 15 x 3 = 45 minutes on watch 1 when watch 1's time is 3:00 pm. Thus watch 2's time is 3:45 pm.

Now let's see watch 3's time. Since watch 3 loses 20 minutes every hour relative to watch 2, so in 3¾ hours, it will lose 20 x 3¾ = 20 x 15/4 = 75 minutes or 1 hour 15 minutes to watch 2 when watch 2's time is 3:45 pm. Thus watch 3's time is 2:30 pm.

Last but not least, let's see watch 4's time. Since watch 4 gains 20 minutes every hour relative to watch 3, so in 2½ hours, it will gain 20 x 2½ = 20 x 5/2 = 50 minutes on watch 3 when watch 3's time is 2:30 pm. Thus watch 4's time is 3:20 pm.

Now if we pit the correct time against watch 4's time, we see that when the correct time is 4 pm, watch 4's time is 3:20 pm. Thus, watch 4 loses 40 minutes in 4 hours, or 10 minutes per hour against the correct time. Thus, in 12 hours (from 12 noon to 12 midnight), watch 4 will lose 10 x 12 = 120 minutes, or 2 hours against the correct time. Therefore, when the correct time is 12 midnight, watch 4's time is 10 pm.

Answer: A

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