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

Author Message
Manager
Joined: 18 Dec 2016
Posts: 106
GMAT 1: 760 Q50 V41
The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗  [#permalink]

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17 Mar 2017, 20:15
2
00:00

Difficulty:

45% (medium)

Question Stats:

39% (00:03) correct 61% (00:01) wrong based on 28 sessions

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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 the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. 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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Math Expert
Joined: 02 Sep 2009
Posts: 52344
Re: The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗  [#permalink]

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18 Mar 2017, 01:08
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

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

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. 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.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52344
Re: The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗  [#permalink]

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05 Jul 2018, 20:24
Re: The sequence a1a1, a2a2, a3a3, ..., anan, ... is such that i∗ai=j∗aji∗ &nbs [#permalink] 05 Jul 2018, 20:24
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