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In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 .

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Hoozan
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In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 . [#permalink] New post   Updated on: 24 Mar 2022, 11:38
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In a certain infinite sequence n, \(n_{1}\) = 7, \(n_{2}\) = 70, \(n_{3}\) = 700 ... \(n_{x}\) = 10(\(n_{x-1}\)), is the integer j a factor of every member of n?

(1) j is a prime number.
(2) j is a factor of more than one member of the sequence
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Originally posted by Hoozan on 23 Mar 2022, 23:31.
Last edited by Hoozan on 24 Mar 2022, 11:38, edited 1 time in total.
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BrentGMATPrepNow
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Re: In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 . [#permalink] New post   24 Mar 2022, 07:37
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Hoozan wrote:
In a certain infinite sequence n, \(n_{1}\) = 7, \(n_{2}\) = 70, \(n_{3}\) = 700 ... \(n_{x}\) = 10(\(n_{x-1}\))

(1) j is a prime number.
(2) j is a factor of more than one member of the sequence


Hi Hoozan,

There needs to be a question in this question :)
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Re: In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 . [#permalink] New post   24 Mar 2022, 08:00
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Hoozan wrote:
In a certain infinite sequence n, \(n_{1}\) = 7, \(n_{2}\) = 70, \(n_{3}\) = 700 ... \(n_{x}\) = 10(\(n_{x-1}\))

(1) j is a prime number.
(2) j is a factor of more than one member of the sequence


If the question is "what is j?" then the answer is E. The primes 2, 5 and 7 are all factors of infinitely many terms in the sequence -- even just looking at the two terms 70 and 700 we can see that those three values of j are possible.

But since no question is provided, I'm just taking a guess at what the question meant to ask. :)
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Re: In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 . [#permalink] New post   24 Mar 2022, 11:39
BrentGMATPrepNow wrote:
Hoozan wrote:
In a certain infinite sequence n, \(n_{1}\) = 7, \(n_{2}\) = 70, \(n_{3}\) = 700 ... \(n_{x}\) = 10(\(n_{x-1}\))

(1) j is a prime number.
(2) j is a factor of more than one member of the sequence


Hi Hoozan,

There needs to be a question in this question :)


Opps! Thanks for bringing it to my attention. I have made the required edits
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Re: In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 . [#permalink] New post   24 Mar 2022, 12:03
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Hoozan wrote:
In a certain infinite sequence n, \(n_{1}\) = 7, \(n_{2}\) = 70, \(n_{3}\) = 700 ... \(n_{x}\) = 10(\(n_{x-1}\)), is the integer j a factor of every member of n?

(1) j is a prime number.
(2) j is a factor of more than one member of the sequence


Thanks for adding the question -- it isn't too different from the one I answered above ("what is j?"), because the only positive factors of every term in the sequence are 1 and 7. So the question is really asking "Is j = 1 or j = 7?" and when we use Statement 1, we know j is not 1, so the question becomes "Is j = 7?" Even with both Statements, j can be 2, 5 or 7, so we can't answer the question, and the answer is E.
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Re: In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 . [#permalink] New post   25 Mar 2022, 01:06
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In a certain infinite sequence n, \(n_{1}\) = 7, \(n_{2}\) = 70, \(n_{3}\) = 700 ... \(n_{x}\) = 10(\(n_{x-1}\)), is the integer j a factor of every member of n?

We are looking at a sequence wherein each subsequent element is 10 times previous element and the sequence starts with 7.

Is the integer j a factor of every member of n? or Is the integer j a factor of 7?, as 7 is the smallest in the sequence.
In other words, is j one of the two - 1 or 7.

(1) j is a prime number.
j could be any prime number.

(2) j is a factor of more than one member of the sequence
The sequence consists of 7, and thereafter, product of 7 and successive multiples of 10.
So, j can be 1, 2, 5 or 7.


Combined,
j could still be 2, 5 or 7.


E
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Re: In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 . [#permalink] New post   24 Jul 2023, 15:26
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Re: In a certain infinite sequence n, n_{1} = 7, n_{2} = 70, n_{3} = 700 . [#permalink]
24 Jul 2023, 15:26
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