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The four members of a jazz quartet all play in different rhy

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The four members of a jazz quartet all play in different rhy [#permalink] New post 21 Feb 2011, 06:43
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The four members of a jazz quartet all play in different rhythms. The pianist plays in 9/8 time, meaning that his downbeats occur every 9/8 of a measure of time. Meanwhile, the saxophonist plays in 7/4 time, the harpist in 5/8 time, and the drummer in plain old 4/4 time (all with respect to the same measure of time as the pianist). If all four musicians start a song together on the same downbeat, how many measures later will all their downbeats occur simultaneously?

(A) 315
(B) 630
(C) 1,260
(D) 2,520
(E) 5,040
[Reveal] Spoiler: OA

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Re: Problem to test your HCF & LCM basics [#permalink] New post 21 Feb 2011, 07:13
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Here's my take on this problem:

This problem basically wants us to calculate the LCM of all the numbers. Since all the beat timings are in fraction, here's a little trick that will help solve the problem quicker.

LCM (fractions)=LCM of all numerators/HCF of all denominators

LCM (\frac{x1}{y1} ,\frac{x2}{y2}, \frac{x3}{y3} , \frac{x4}{y4})= \frac{LCM (x1 , x2 , x3 , x4)}{HCF (y1 , y2 , y3 , y4)}

Therefore, LCM (\frac{9}{8} , \frac{7}{4}, \frac{5}{8}, \frac{4}{4}) = \frac{LCM (9,7,5,4)}{HCF (8,4,8,4)}= \frac{(9*7*5*4)}{(4)}= 315.

Answer: A.

A note: To find HCF of given fractions, we can manipulate the above formula just a little:

HCF(fractions)= HCF of all numerators/LCM of all denominators.

HCF((\frac{x1}{y1} ,\frac{x2}{y2}, \frac{x3}{y3} , \frac{x4}{y4})= \frac{HCF (x1 , x2 , x3 , x4)}{LCM (y1 , y2 , y3 , y4)}
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Re: Problem to test your HCF & LCM basics [#permalink] New post 23 Feb 2011, 13:44
This problem seems to be flawed and should be reworked IMHO. For starters 315 measures of 9/8 equals 2835 half beats (1/8) so it is not a multiple of any n of measures in 4/4 or any other full beat based time signature which at the very least would require an even number of half beats. I think the problem should also be specific as to the time signature of the measures we a to count. The wording implies 9/8 (which doesn't work) but the solution seems to be using 4/4 (not sure here).

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Re: Problem to test your HCF & LCM basics [#permalink] New post 23 Feb 2011, 20:49
Where is the source for this? I think it assumes too much knowledge. What is a measure? Downbeat?
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Re: Problem to test your HCF & LCM basics [#permalink] New post 24 Feb 2011, 20:39
Philmess wrote:
This problem seems to be flawed and should be reworked IMHO. For starters 315 measures of 9/8 equals 2835 half beats (1/8) so it is not a multiple of any n of measures in 4/4 or any other full beat based time signature which at the very least would require an even number of half beats. I think the problem should also be specific as to the time signature of the measures we a to count. The wording implies 9/8 (which doesn't work) but the solution seems to be using 4/4 (not sure here).

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Actually, we dont really need to know the definitions of the music terms. Neither is it important to know whether the definitions are correct. We just need to find out what the question asks us to do ie, find out the LCM of the different timings. Only thing is that we need to deal with fractions, which could make things a little trickier. The same concept can be tested in an easier way, not involving complex terms or even fractions:

The 3 bells in a temple toll at an interval us 3,5 and 10 minutes respectively. Suppose today all three bells will toll at 9 am, at what time will the three bells toll together next?

So your approach here will be to take the LCM of the intervals, convert it into hours, add it to 9 and you have your answer.
In the original problem, the approach is the same. Only thing is that since it involves fractions, you have to apply your knowledge just a little bit more.
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Re: Problem to test your HCF & LCM basics [#permalink] New post 21 Dec 2013, 23:34
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Re: Problem to test your HCF & LCM basics   [#permalink] 21 Dec 2013, 23:34
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