Geertrude's Mother

[sourabh33]

[SoCan]

With an 8 minute time difference, the clocks will show the same time every 7.5 days (first clock is making up 8 minutes an hour, and needs to catch up 1440 minutes, and 1440/8 = 180 hours or 7.5 days). We also know that the first clock gains 2 hours a day, so we know that when these clocks match up after 7.5 days, they'll show a time of 15:00 (useful to think of a 24 hour clock since we're interested in midnight). Keep adding 15 hours for every 7.5 days to see when they finally match up at midnight (alternatively, find how many times 15 goes into the LCM of 15 and 24 - 120 - and multiply that number by 7.5):

7.5 days - 15:00
15 days - 6:00
22.5 days - 21:00
30 days - 12:00 (noon, not midnight)
37.5 days - 3:00
45 days - 18:00
52.5 days - 9:00
60 days - 24:00 (midnight)

So E.

[sourabh33]

Brilliant! how much time did you take to solve this?

[SoCan]

Too long. At first I thought I had solved it just by figuring out when the first clock would catch up to the second clock, which took me about a minute. Then I checked the work and realized that wasn't true, and tried to figure out a different way to solve it. When I couldn't do that, I went back to the 7.5 days intermediate solution and used that. Probably 4-5 minutes in all.

[kevincanspain]

First clock loses 3 min/hour or 1 hour/ 20 hours or 12 hours/ 240 hours

Second close needs only 3/5 of this time to gain 12 hours i.e. 144 hours

LCM (240,144) =720 hours = 30 days

E

[SoCan]

First clock loses 3 min/hour or 1 hour/ 20 hours or 12 hours/ 240 hours

Second close needs only 3/5 of this time to gain 12 hours i.e. 144 hours

LCM (240,144) =720 hours = 30 days

E

You get the same answer because of the "more than three" wording, but it's not actually 30 days. At 30 days, they both hit noon at the same time. You need to do LCM (480,288) instead because you need to gain 24 hours again, not 12.

[kevincanspain]

It says 'strike 12 at midnight', but does not specify whether it has to be 12 o'clock midnight.