Geertrudes grandmother has two grandfather clocks. One loses

Question

Geertrudeâ€™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

shampoo · Answer

not sure if I am doing this right. In 24hr the difference between the clocks is 192 min. The clocks will struck togather when the differnce between them is 12hrs or 720min. 192x4= 768. So clocks will struck togather in less then 4 days?

A.

shampoo · Answer

umm, now if they have to struck togather at midnight again then the difference should be 24hrs between them or 1440min. 192 * 7 = 1344.
so B?

ps_dahiya · Answer

In 30 hours difference between clocks will be 1 hour i.e every 30 hours their minute hands coincide.

So in 24 * 30 = 720 hours difference between them will be none i.e their minute hands and hour hands will conincide.

Answer = 720 hours = 30 days = 4 weeks 2 days
Above I am assuming after how much time they will meet again at midnight.

But if question asks " after how much time they wil meet again at 12 (either mid night or noon) Then answer should be 2 weeks and 1 day.
Answer = 360 hours = 15 days = 2 weeks 1 day

haas_mba07 · Answer

To find the next time these clocks strike together we need to find the first time when the times are equal.. 

LCM (57, 65) = 3x19x5x13 = 3705 (approx 60 hrs)
 
60 hrs < 1 week.

Answer : A.

Dilshod · Answer

what if the question is asking when do the both clock struck at one time, and it doesn't matter if it is midnight or midtoon:
In that case the answer might also be 7.5 days, 15, 22.5 etc...
if only midnight, than the answer is 15, 30,...

1 day:
clock 1 - 11.48
clock 2 - 14.00

the difference is 192 minutes.
Hence, with each succeeding day 192 minutes should be added to that difference: x days = x*192minutes.
in order for the both clocks to struck at one time the difference should be 24 hours or 24*60 minutes.

Thus, 7.5 days: 25*60/192.

haas_mba07 · Answer

hmmm.. good point. I didn't realize the question asked for the next "midnight".

MA · Answer

you are correct. in 60 hours it will be 12.00 noon. so it takes 120 hours or 5 days to be 12.00 idnight. 

but the answer still remains A.

Dilshod · Answer

hi MA,
Think again...

Or just plug 180, 540 ....hours for your case(when it doesn't matter whether it is midnight or noon)
And 360,720... (if it must be only at midnight)

ps_dahiya · Answer

Help me understand guys. How can they struck 12:00 Noon after 30 hours or 12:00 Midnight after 60 hours.

After 30 hours time in clock 1 will be 4:30 and in clock 2 will be 3:30
After 60 hours time in clock 1 will be 9:00 and in clock 2 will be 7:00

Answer should be either C (If asked: When the clocks will show same time. For example one shows 3:00 AM and other shows 3:00 PM) or E (If asked: When the clocks will show 12:00 either noon or midnight).

This problem is kind of a relative velocity. 5 -3 = 2 minutes. It means clock move only 2 minutes in 1 real hour. Then how much real time it will take to move 24 hours. In 720 real minutes, this clock will run only 24 hours.

Please, correct me if I am wrong.

See attached excel spreadsheet, I tried to calculate using excel formulae.

Dilshod · Answer

Hi,
relax
It cannot be 30 or 60.
it should start from 7.5(15, 22.5, 30....) days(if midnight is not required), 
or
15,30,45.... days(if midnight is required)

Anyway, the answer may be C,D,E, depending on what the author meant. the question needs to be clarified.

kevincan · Answer

I thought the question was clear, but in view of the confusion, I'll explain. When I said "do so", I meant "strike 12 at midnight". I don't know what else this could mean, but it's great to see what wording works and what doesn't!

Dilshod · Answer

Hi,
it could mean, at least for me, "both struck", not neccessarily "both struck at midnight".

KevinCan,
where are you getting these questions from?
they remind me the questions i got in my real test.

ps_dahiya · Answer

OK now Kevin has claified the question.

Easier method is:

Let after x real hours both clocks show the same time.

Time lost by clock 1 in hours = 3x
Time lost by clock 2 = 5x

Difference in time lost should be 24 hour = 5x - 3x = 24 * 60
So x = 720
Now yet finished.
Time in clock 1 after 720 hours = (720 - 720 *3/60)/24 = 28 days and 12 hours. In real time 30 days have elapsed but in clock only 28.5 days have elsapsed. This means its not midnight yet, its noon.

For midnight double the hours i.e x = 2* 720 = 1440 = 60 days.

ANS = 8 weeks and 4 days. i.e E

kevincan · Answer

I'm making them up for a book. I'm a GMAT trainer at Kaplan. I hope you enjoy them and I appreciate all of your comments/suggestions! Feel free to suggest topics/problem areas for new questions!

kevincan · Answer

You say that both clocks lose time- this is not the case!

ps_dahiya · Answer

I misread the question. In this case
we take 3x+5x = 24 * 60
 x= 180 hours.
After 180 hours both clock will show 03:00 AM
After 180*2 hours both clock will show 06:00 AM 
and so on....
After 180 * 8 = 1440 hours both will again show 12:00 AM

BTW answer is still coming same...... 1440/24 = 60 days.

kevincan · Answer

Clue: How many hours must elapse for the clock that is losing time to lose exactly 12 hours? Is this number of hours a mutliple of 24? This is important to ensure that it marks the right time at midnight.

Repeat questions for the other clock

Dilshod · Answer

kevincan,
am I still mising something?
the answer can be both C and E.
15 days - >2 weeks
30 days - >3 weeks

kevincan · Answer

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.

Geertrudes grandmother has two grandfather clocks. One loses

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