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Geertrudes grandmother has two grandfather clocks. One loses

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Dilshod
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   Updated on: 18 Jul 2006, 01:03
kevincan wrote:
How many full weeks must go by before both clocks strike 12 at midnight on the same night. Clocks generally strike 12 twice a day, once when they mark 12PM and once when they mark 12AM.


Oh I get it.
Both clock SHOULD show 12 PM at one time.
One clock should loose 12*x hours, while the other one should gain 12*x hours, where x should be even integer.
So the least time that should pass is:
1440 hours should pass for the slower clock to loose 24 hours, and the same number of hours should pss for the faster clock to gain additional 24 hours.
hence 1440, 1440*2*x.....

correct?

Originally posted by Dilshod on 18 Jul 2006, 00:56.
Last edited by Dilshod on 18 Jul 2006, 01:03, edited 1 time in total.
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 01:00
Dilshod wrote:
kevincan wrote:
How many full weeks must go by before both clocks strike 12 at midnight on the same night. Clocks generally strike 12 twice a day, once when they mark 12PM and once when they mark 12AM.


Oh I get it.
Both clock SHOULD show 12 PM at one time.
One clock should loose 12*x hours, while the other one should gain 12*x hours, where x should be even integer.
So the least time that should pass is:
slower clock should loose 24 hours, while the faster should gain 24 hours.
Hence, 1440 hours should pass.

correct?



x need not be an even integer, nor do the two clocks have to be off the same number of hours
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 01:11
kevincan wrote:
Dilshod wrote:
kevincan wrote:
How many full weeks must go by before both clocks strike 12 at midnight on the same night. Clocks generally strike 12 twice a day, once when they mark 12PM and once when they mark 12AM.


Oh I get it.
Both clock SHOULD show 12 PM at one time.
One clock should loose 12*x hours, while the other one should gain 12*x hours, where x should be even integer.
So the least time that should pass is:
slower clock should loose 24 hours, while the faster should gain 24 hours.
Hence, 1440 hours should pass.

correct?



x need not be an even integer, nor do the two clocks have to be off the same number of hours

In that case how are you going to maintain that both clocks will show exactly 12.00 midnight?

if all that is required is exactly 12 strikes, the answer may be
720 hours as well.
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 01:14
All that is required is 12 strikes! I've reworded thw question to make it cleaer. Tell me what you think!
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 01:21
kevincan wrote:
All that is required is 12 strikes! I've reworded thw question to make it cleaer. Tell me what you think!

IMO, it is still hard to get from the question that all that needed is 12 strikes. e.g., that one clock may show 12.00am while the other 12.00pm.

Why don't you add smth. like "all that requied is 12 strikes"?
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 01:28
If a clock strikes 12, it could be noon or midnight!
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   Updated on: 18 Jul 2006, 01:39
kevincan,
Quote:
If a clock strikes 12, it could be noon or midnight!

why not?

You've just said:
Quote:
All that is required is 12 strikes!

Originally posted by Dilshod on 18 Jul 2006, 01:34.
Last edited by Dilshod on 18 Jul 2006, 01:39, edited 1 time in total.
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 01:38
OK,
can you PM me the answer(# of hours)?
Without it, it is still hard for me to clearly understnad what the question is asking for?
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 09:09
Hi Kevin,
thanks for the PM.

Offtopic: i wonder, have you ever taken GMAT?
I just remebered that I got almost the same question on my Real exam(7th or 8th question) with slightly different numbers.
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 15:39
kevincan wrote:
Geertrude’s grandmother has two grandfather clocks. One loses 3 minutes every hour; in other words, it will show that 57 minutes have elapsed when in fact exactly one hour has gone by. The other gains 5 minutes every hour. Geetrude and her grandmother always open a bottle of champagne when the two clocks strike 12 at midnight on the same night. On all other nights, they open a bottle of apple cider. Last night, they opened a bottle of champagne. How many full weeks must go by before they can do so again?

(A) none (B) one (C) two (D) three (E) more than three


The next time the first clock will ring exactly at midnight is when it loses 24 hrs. Hence 3m = 24*60 => m = 24*20 hrs.

Similarly, the next time the second clock will ring at midnight is when it gains 24 hrs. Hence 5n = 24*60 => n = 24*12 hrs.

The next time the two clocks ring together is at the LCM of m and n = 24*4*3*5 = 24*60 hrs = 60 days (more than 3 weeks)

Answer (E)?

<phew> what a question!
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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink] New post   18 Jul 2006, 16:32
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x=number of hours

19/20 * x must be divisible by 12

Hence X is a multiple of 20*12=240.

13/12 * x must be a multiple of 12 => x must be a multiple of 12*12=144.

LCM (144,240) = 720
x=720 (since 720 is divisible by 24, it is midnight, when the clock strikes).

[720:24=30 days > 3 weeks]

=> E.



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Re: Geertrudes grandmother has two grandfather clocks. One loses [#permalink]
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