Mark owns four low quality watches. Watch1 loses 15 minutes every hour

The way I solved it was by looking at it from Relative speed perspective:

W1 = -15min/hr wrt to the clock
∴ W2 - W1 = Relative speed = +15min/hr
∴ W2 + 15 = 15
∴ W2 = 0

Similarly, W3 = 20min/hr, W4 = 40min/hr,

Now, all clocks are set to 12noon. To go to 12midnight, we have to account for 12 hours
So, W4 will show:
= 40min/hr * 12 hours
W4 = 480 mins
W4 = 480mins/60mins = 8hours

∴ W4 should show 8pm~!

But as you can see there is no option like that. Please can someone tell me where did I go wrong?
Thanks!

Hi,
we will have to compare two watches then change it to hour...
1) Watch1 loses 15 minutes every hou
O-1 hr , W1-45min or 3/4hr...
2)Watch2 gains 15 minutes every hour relative to watch1 ..
when W1-1hr, W2-1hr 15min or 5/4hr....
now lets compare the three..
O-4/3,W1-1,W2-5/4...
3) Watch3 loses 20 minutes every hour relative to watch2..
when W2-1hr, W3=2/3hr..
now lets compare O,W2,W3..
O-4/3*4/5, W2-1hr,W3-2/3..
4) now the last one
watch4 gains 20 minutes every hour relative to watch3..
when W3-1, W4-4/3..
lets compareO,W3 and W4..
O-4/3*4/5*3/2, W3-1hr,W4-4/3hr..

finally lets take only O and W4
O-4/3*4/5*3/2=8/5,W4-4/3hr..
so when O=1, W4=4/3*5/8=5/6..
and when O=12hr, W4=5/6*12=10 hr..

therefore when original shows 12, the W4 will show 10..
ans A

the speeds are relative to the other when one covers 1 hr..
so you cannot simply add and subtract, but convert the ratios as shown above..

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.