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The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗

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The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗  [#permalink]

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New post 17 Mar 2017, 21:15
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The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗ai=j∗aj for any pair of positive integers (i,j)(i,j). If a1a1 is a positive integer, which of the following could be true?
I. 2∗a100=a99+a982∗a100=a99+a98
II. a1a1 is the only integer in the sequence
III. The sequence does not contain negative numbers

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III


Question Tag: - M17-25

I encountered this question on a gmatclub quant test....

the official explanation states that 'II' is a 'Could be True' case. However, I think that 'II' is always true and belongs to 'Must be True' or 'Always be true' case. I am not able to think of any other case that can violate this condition.

Can any expert (@Bunuel) enlighten me on this one?

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗  [#permalink]

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New post 18 Mar 2017, 02:08
gmat2k17 wrote:
The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗ai=j∗aj for any pair of positive integers (i,j)(i,j). If a1a1 is a positive integer, which of the following could be true?
I. 2∗a100=a99+a982∗a100=a99+a98
II. a1a1 is the only integer in the sequence
III. The sequence does not contain negative numbers

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III


Question Tag: - M17-25

I encountered this question on a gmatclub quant test....

the official explanation states that 'II' is a 'Could be True' case. However, I think that 'II' is always true and belongs to 'Must be True' or 'Always be true' case. I am not able to think of any other case that can violate this condition.

Can any expert (@Bunuel) enlighten me on this one?


Discussed here: series-a-n-is-such-that-i-a-i-j-a-j-for-any-pair-of-96538.html and here: m17-184131.html

Also, please read this: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Joined: 02 Sep 2009
Posts: 47923
Re: The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗  [#permalink]

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New post 05 Jul 2018, 21:24
Re: The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗ &nbs [#permalink] 05 Jul 2018, 21:24
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