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Aaron, Ben, and Cliff all make resolutions to exercise more in the new

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Bunuel
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Aaron, Ben, and Cliff all make resolutions to exercise more in the new [#permalink] New post   02 Dec 2019, 00:43
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Aaron, Ben, and Cliff all make resolutions to exercise more in the new year. Aaron resolves to exercise on every fourth day, Ben resolves to exercise on every seventh day, and Cliff resolves to exercise on every tenth day. If they follow their resolutions exactly, what is the probability that they all exercised on a randomly selected day, assuming this is not a leap year?


A. \(\frac{2}{365}\)

B. \(\frac{1}{280}\)

C. \(\frac{1}{73}\)

D. \(\frac{13}{65}\)

E. \(\frac{28}{73}\)


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LevanKhukhunashvili
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Aaron, Ben, and Cliff all make resolutions to exercise more in the new [#permalink] New post   02 Dec 2019, 01:18
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My way of reasoning

\(P=\frac{{Favorable outcomes}}{{Possible outcomes}}\)

1) Favorable outcomes: we need the LCM for \(2^2\), \(7\) and \(2*5\) LCM=140; \(\frac{365}{140}=2.\) SO we have got only two days when they all exersice
2) Posible outcomes: normal year does have 365 days

\(\frac{2}{365}\)

IMO
Ans: A
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Re: Aaron, Ben, and Cliff all make resolutions to exercise more in the new [#permalink] New post   02 Dec 2019, 04:18
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Explanation:

Only 2 Days are there on which all 3 will exercise.
i.e. 140 th & 280th Day.
Probability : Favourable outcome/ total no. of outcomes
= 2/365
IMO-A

:please Please give kudos, if you find my explanation good enough :please
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Re: Aaron, Ben, and Cliff all make resolutions to exercise more in the new [#permalink] New post   26 Feb 2021, 21:42
LCM question. see cyclicity between the 3 cases

the days coincide every LCM, thus every 140 days from the start they coincide. 140*2 is the only max cases with 365 days.

Thus 2/365.
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Re: Aaron, Ben, and Cliff all make resolutions to exercise more in the new [#permalink]
26 Feb 2021, 21:42
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