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M17-25

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Re: M17-25  [#permalink]

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New post 29 Apr 2018, 17:49
Now It's working fine! Ty Bunuel!!!
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Re: M17-25  [#permalink]

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New post 19 May 2018, 12:36
Bunuel wrote:
Official Solution:


II. \(a_1\) is the only integer in the sequence. If \(a_1=1\), then all other terms will be non-integers, because in this case we would have \(a_1=1=2a_2=3a_3=...\), which leads to \(a_2=\frac{1}{2}\), \(a_3=\frac{1}{3}\), \(a_4=\frac{1}{4}\), and so on. Hence this option could be true.

III. The sequence does not contain negative numbers. Since given that \(a_1=\text{positive integer}=n*a_n\), then \(a_n=\frac{\text{positive integer}}{n}=\text{positive number}\), hence this option is always true.



Why does the explanation for II say "could be true" and not "always true" (like it does for III)?
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Re: M17-25  [#permalink]

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New post 19 May 2018, 14:01
aserghe1 wrote:
Bunuel wrote:
Official Solution:


II. \(a_1\) is the only integer in the sequence. If \(a_1=1\), then all other terms will be non-integers, because in this case we would have \(a_1=1=2a_2=3a_3=...\), which leads to \(a_2=\frac{1}{2}\), \(a_3=\frac{1}{3}\), \(a_4=\frac{1}{4}\), and so on. Hence this option could be true.

III. The sequence does not contain negative numbers. Since given that \(a_1=\text{positive integer}=n*a_n\), then \(a_n=\frac{\text{positive integer}}{n}=\text{positive number}\), hence this option is always true.



Why does the explanation for II say "could be true" and not "always true" (like it does for III)?


The question asks: which of the following COULD be true. If an option is true, is possible, even for one sequence then it fits.

I is not true for this sequence at all. So it's out.
II COULD be true in certain case, so it fits.
III is ALWAYS true, so it also fits.

Hope it's clear.
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Re: M17-25  [#permalink]

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New post 03 Aug 2018, 14:52
For the statment 2, instead of taking a1 as 1 if we take it as 2 then there woudl be 2 integers in this case. Hence the statement can be false aswell
a2 = a1/2 => 2/2 => 1

So why option 2 is correct?
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New post 04 Aug 2018, 00:17
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salilgupta4180 wrote:
For the statment 2, instead of taking a1 as 1 if we take it as 2 then there woudl be 2 integers in this case. Hence the statement can be false aswell
a2 = a1/2 => 2/2 => 1

So why option 2 is correct?


Notice that the question is which of the following COULD be true, not MUS be true. II COULD be true if a1 = 1. In this case a1 will be the only integer in the sequence.
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Re: M17-25 &nbs [#permalink] 04 Aug 2018, 00:17

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