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EgmatQuantExpert
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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch Updated on: 16 Aug 2024, 08:54
Originally posted by EgmatQuantExpert on 30 Jul 2018, 21:54.
Last edited by Bunuel on 16 Aug 2024, 08:54, edited 2 times in total.
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95% (hard)

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57% (03:01) correct 43% (03:19) wrong based on 341 sessions

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Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch loses 10 seconds in every 2 hours. If both watches are set to the correct time at 1 a.m. Sunday, then at what earliest time they will have a difference of 9 minutes among them?

A 7 a.m. Wednesday
B. 10 a.m. Wednesday
C. 7 p.m. Wednesday
D. 10 p.m. Wednesday
E. 7 a.m. Thursday[/list]


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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch 10 Aug 2018, 05:58
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Solution



Given:
    • Seb’s watch gains 5 seconds in every 3 hours
    • Lewis’ watch loses 10 seconds in every 2 hours
    • Both watches are set to the correct time at 1 a.m. Sunday

To find:
    • At what earliest time the watches will have a difference of 9 minutes among them

Approach and Working:
    • A difference of 9 minutes is equivalent to 60 x 9 = 540 seconds.

Now, Seb’s watch gains 5 seconds in every 3 hours.
    • Hence, in 1 hour, it will gain \(\frac{5}{3}\) seconds.

Similarly, Lewis’ watch loses 10 seconds in every 2 hours.
    • Hence, in 1 hour, it will be losing 5 seconds.

    • Therefore, in 1-hour time, the difference created between the watches = \(\frac{5}{3}\) – (-5) = \(\frac{20}{3}\) seconds

Now, we can say, to create a difference of \(\frac{20}{3}\) seconds, we need 1 hour.
    • So, to create a difference of 540 seconds, we need 540/(\(\frac{20}{3}\)) = 81 hours.

From 1 a.m. Sunday, 81 hours forward will be 10 a.m. Wednesday.

Hence, the correct answer is option B.

Answer: B


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ankitsaroha
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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch 30 Jul 2018, 22:11
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B

9 minutes = 540 seconds
In every 6 hours, difference increases by 40 seconds.
In 78 hours, by 520 seconds

Only 20 more seconds required.

In next 3 hours, Seb's watch would gain 5 seconds and Lewis's watch would lose 15 seconds (10 seconds in 2 hours is same as 5 seconds in 1 hour)
Difference = 5 + 15 = 20 seconds

Total hours passed = 78+3 = 81
81 hours from 1am Sunday is 10am Wednesday.

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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch 30 Jul 2018, 22:57
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9 minutes = 9*60 = 540 seconds.

Seb’s watch gains 5 seconds in every 3 hours
Every hour Seb's match gain 5/3 seconds

Lewis’ watch loses 10 seconds in every 2 hours
Every hour Lewis’ watch loses 10/2 = 5 seconds

Relative difference per hour = 5 + 5/3 = 20/3 Seconds

Time taken to gain 540 seconds = 540/(20/3) = 540*3/20 = 81 hours

81 Hours = 72 Hours (3 24 Hour day) + 9 Hours =>

1 AM + 9 Hours = 10 AM, which is 3 days later i.e. Wednesday.

Option B
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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch 13 Sep 2019, 08:05
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Hello please help me out.is my approach correct.
3h=> 5sec increase,so
24h=> 40 sec increase.

Similarly 2h=> 10 sec decrease
24hr => 120 sec decrease
So for 48 hrs diff will be =150
72hrs difference will be =240
I am not getting answer like this,
Why this is wrong.

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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch 13 Sep 2019, 09:08
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harinageshwar
Hello please help me out.is my approach correct.
3h=> 5sec increase,so
24h=> 40 sec increase.

Similarly 2h=> 10 sec decrease
24hr => 120 sec decrease
So for 48 hrs diff will be =150
72hrs difference will be =240
I am not getting answer like this,
Why this is wrong.

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You are wrong because you have assumed that both the increase and decrease are happening over a 2 days , wheras they're actually happening simultaneously.
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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch 16 Aug 2024, 08:51
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The point of this question is that recognizing the least common multiple, 6, simplifies the problem.

Every 6 hrs Seb's watch gains 10 seconds and Lewis's watch loses 30 seconds, for a total difference of:

40s/6 hrs

Since 9 minute difference = 540 seconds, the number of hours required to generate this difference is:

540s/(40s/6hrs) = 13.5*6 =

81 hours.

Since 72 hours = 3 days, 3 days and 9 hours must pass.

So, Wednesday at 10 am

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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch 09 Sep 2025, 23:12
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