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

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Joined: 21 Aug 2014
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Mark owns four low quality watches. Watch1 loses 15 minutes every hour  [#permalink]

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04 Jul 2015, 08:54
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95% (hard)

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48% (03:18) correct 52% (03:18) wrong based on 137 sessions

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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
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Joined: 02 Aug 2009
Posts: 6974
Re: Mark owns four low quality watches. Watch1 loses 15 minutes every hour  [#permalink]

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04 Jul 2015, 09:18
4
2
Patronus 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

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
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Re: Mark owns four low quality watches. Watch1 loses 15 minutes every hour  [#permalink]

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09 Jul 2016, 11:53
3
2
Another approach which is similar to one posted before

Let h be elapsed actual hrs

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

H = 12 hrs so W4 would show 5*12/6 = 10hrs from zero
General Discussion
Current Student
Joined: 21 Aug 2014
Posts: 138
GMAT 1: 610 Q49 V25
GMAT 2: 730 Q50 V40
Mark owns four low quality watches. Watch1 loses 15 minutes every hour  [#permalink]

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04 Jul 2015, 08:57
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!
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Posts: 6974
Re: Mark owns four low quality watches. Watch1 loses 15 minutes every hour  [#permalink]

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04 Jul 2015, 09:21
Patronus wrote:
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!

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..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Mark owns four low quality watches. Watch1 loses 15 minutes every hour  [#permalink]

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09 Jul 2016, 11:44
3
Way I solved it

W1 - loses 1/4th of hr every hr - 12:00-12:00 - 12 hrs , loses 12/4 =3 hrs so time on w1 would be 09:00 pm
W2 - gains 1/4th of hr every hr wrt W1 - 09:00 pm on W1 -> 9 hrs -> 9/4 hrs gained = 8/4 + 1/4 = 2hrs 15 mins gained => time = 11:15 pm
W3 - loses 1/3rd of hr every hr wrt W3 - 11:15 pm = 11 + 1/4 hrs = 9 + 9/4 hrs ; divide by 3 => 3 + 3/4 hrs lost => 3 hrs 45 mins lost => time = 07:30 pm
W4 - gains 1/3rd of hr every hr wrt W3 - 07:30 => 7 + 1/2 hrs = 6 + 3/2 hrs ; divided by 3 => 2 + 1/2 hrs => time = 07:30 + 2.5 hrs = 10:00 pm
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Mark owns four low quality watches. Watch1 loses 15 minutes every hour  [#permalink]

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22 May 2018, 18:00
1
Patronus 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.

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Mark owns four low quality watches. Watch1 loses 15 minutes every hour &nbs [#permalink] 22 May 2018, 18:00
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