A certain hall contains two cuckoo clocks. If the first

Question

A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 10 times per hour, and both clocks begin chirping at 1:15 PM, at what time will the first clock have chirped three times as many times as the second clock can per hour?

A. 1:24 PM
B. 2:05 PM
C. 2:30 PM
D. 2:45 PM
E. 4:15 PM

A. 1:24 PM
B. 2:05 PM
C. 2:30 PM
D. 2:45 PM
E. 4:15 PM

Javoni · Answer

I would go with the (D), below I expound upon my choice.
First clcock chirps 20 times per hour , that means 20/60 = 1/3 times per minute.
Second clock chirps 10 times per hour, that would be 10/60 = 1/6 times per minute. 
We are asked: at what time will the first clock have chirped three times as many times as the second clock can per hour, or in other words 3 times as many as the second one 3*1/6 = 1/2 and we get the proportion:
1 - 1/3
x - 1/2 from here x = 3/2 =1*(1/2), i.e. 1 hour 30 minutes or 1:15 PM + 1 hour 30 minutes = 2:45
Please, feel free to correct me, if I went awry

joylive · Answer

I think your solution makes sense

jzpat · Answer

I agree with the solution.
So the slower clock can tick 10 times per hour, and according to the problem we want to know when the faster one can potentially tick 10*3 times= 30
Hence 30/20=1.5 or one hour and a half later. Adding this to 1:15 pm the result should be D, or 2:45 pm.

TehMoUsE · Answer

Good question! Caught me offguard. Notice the highlighted

"at what time will the first clock have chirped three times as many times as  the second clock CAN (!!) per hour ?"

It is easy to interpret the question as "what time has clock A chirped 3 times more than clock B?" - do some calculations and come up with E

But, We basically want to know when the first clock has chirped  3*10=30 times

Clock A chirps 20 times each hour ----> 1 time each 3min -----> 30 times in 90min

1:15PM + 90min = 2:45PM

Correct Answer: D

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Solution: D.

Don't be confused by the tricky wording: at its core this is a very simple problem. The second clock chirps 10 times per hour, so we want to know at what point the first clock has chirped three times that, or 3 * 10, which is 30. If the first clock can chirp 20 times per hour, then it will take 1.5 hours to chirp 30 times. 1.5 hours is the same as 90 minutes, so the first clock will have chirped 30 times 90 minutes after 1:15, which would be 2:45 PM. (D).

Lucky2783 · Answer

Hi  Bunuel ,

Had the question been : when is the first time first clock have chirped three times as many times as the second clock?
How will do that ?

Thanks!
Lucky

Lucky2783 · Answer

I think it will never happen . First clock will always have chipred just twice the times the Second Clock Chirp. 
Let me know if i am wrong.

thanks

Harley1980 · Answer

If we infer that cuckoo chirps evenly per time, than correct answer will be 9 minutes. Because first cuckoo chirps 1 time in 3 minutes and second 1 in 6 minutes. 
So in 9 minutes first cuckoo shirps 3 times and second 1 time.

If we infer that cuckoo chirps 20 times once in hour than they will chirp simultaneously and this task has no solution:
1 hour 20:10 
2 hour 40:20 
an so on.

I reread solutions twice but can't understand why we infer that cuckoos chirp two times per hour and make equal number of sounds every half an hour?
Am I miss something?

chetan2u · Answer

Hi,
Your logic is absolutely correct but we are asked "at what time will the first clock have chirped three times as many times as the  second clock can per hour ?"... per hour is the catch word..
second clock chirps 10 times in one hour... so the question is basically asking by when will the first clock chirp 30 times (thrice 10 chirps)..
first will take 1 hr 30 min for this .. 
add it to 1:15.. ans 2 :45 
ans D
hope it helped

Harley1980 · Answer

Wow, thanks  chetan2u . As usual I miss some crucial words from question (

ScottTargetTestPrep · Answer

Since the second clock can chirp 10 times per hour and we want the first clock to chirp 3 times as many, we want the first clock to chirp 30 times. Since the first clock chirps 20 times per hour (60 minutes), it will chirp 30 times in 60/20 x 30 = 3 x 30 = 90 minutes. Therefore, at 1:15 PM + 90 minutes = 2:45 PM, the first clock will have chirped three times as many times as the second clock can per hour.

Answer: D

BinodBhai · Answer

The ques asks if 2nd clock chirps 10 times per hour, when will 1st clock chirp 3 times of it.. i.e. 30 chirps -

20 chirps ---- 60 mins
30 chirps ---- ? mins

Cross multiply

Mins = 30x60/20 = 90 mins .. so 1 hr 30 mins from 1:15 is 2:45 (D)

Kushagra1Luthra · Answer

I have a doubt -
For clock 1 - 20 chirp per hour means — 3 min per chirp
For clock 2 — 10 chirp per hour means — 6 min per chirp

So if they start at 1:15
Clock 1 
1:18 - 1st chirp
1:21 - 2nd chirp
1:24 - 3rd chirp
Clock 2
1:21 - 1st chirp
1:27 - 2nd chirp

So at 1:24 clock 1 chirp 3 times where as at 1:24 clock 2 would have chirped only 1 time so why not 1:24 is the answer ?

Bunuel · Answer

The phrase "per hour" means  in one full hour . So if the second clock chirps 10 times per hour, then three times that is  30 chirps .

The question is asking:  when will the first clock reach 30 chirps?  Since it chirps at 20 per hour, it takes  1.5 hours  to do that. So from 1:15 PM, that happens at  2:45 PM . That's the whole point.

A certain hall contains two cuckoo clocks. If the first

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A certain hall contains two cuckoo clocks. If the first

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