Problem Solving

Gertruede's grandma had three grandfather clocks. One clock gained 5 minutes every hour. The other lost 3 minutes every hour. The third one was right on time. How frequently will all the three clocks show the same time on midnight?

(1) 72 days
(2) 0 days
(3) 30 days
(4) 2 days
(5) 230 days


I will publish the OA later cos I know most will get this one. But I think this is a 700+ question. Please post your answer and the time you took to get the answer and also the rating of this question (500+/600+/700+)

IMO A

Kindly mention the OA

IMO 30 days....

here i am assuming that 12 midnight is same as 12 noon

now first clock looses 5 mins per hour=> 120 mins per day or 2 hrs per day

second clock looses 3 mins per hour => 72 mins in a day or 1.2 hrs in a day

now for loosing 12 hrs
first clock takes 6 days
second clock takes 10 days
now LCM is 30 for 6 and 10

I was inclined to take 24 hr cycle but since none of the answer matches that choice so i assumed an analogue clock.

OA is C.
The approach is right (taking LCMs). But this question is definitely 700+. What do you guys think?

yep .. IMO C.

Clock 1 advances 120 mins per day.
Clock 2 lags 72 mins per day.
Clock 3 is on time.

Implies,

Clock 1 needs 12 days to make it to midnight including the delay.
Clock 2 needs 20 days to make it to midnight including the delay.

By running through the options I got 30 days.

Can someone give a better approach to this solution?

Should the question be rephrased because I think to reach the midnight it takes 60 days for all the clocks to be in sync.


Regards,

Pranay