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If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1

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If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

[Reveal] Spoiler:
I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

Please advise.
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Jun 2014, 04:05, edited 1 time in total.
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If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.


I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

Please advise.


No, B is not correct. It's straight E: if p=3 then every term in S is divisible by p but if p=11 then some terms in S are divisible by p (for example 99 and 9999) and some are not (for example 9 and 999). Not sufficient.

Answer: E.

hope it's clear.
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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+1 E

Question tends to make you just go for 3 & you choose C but as Bunuel pointed out if you use 11 the assumption fails
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 22 Jan 2013, 05:43
what would be the equations for each statement?
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 22 Jan 2013, 08:20
If you were to test examples to satisfy the equations what would they be examples for each statement.
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 22 Jan 2013, 08:24
Expert's post
fozzzy wrote:
If you were to test examples to satisfy the equations what would they be examples for each statement.


Since the answer is E, then the examples given in my post to show that the two statements taken together are not sufficient to answer the question, would also serve to discard each statement.
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 22 Dec 2013, 07:01
Bunuel wrote:
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.


No, B is not correct. It's straight E: if p=3 then every term in S is divisible by p but if p=11 then some terms in S are divisible by p (for example 99 and 9999) and some are not (for example 9 and 999). Not sufficient.

Answer: E.

hope it's clear.


Hello Bunuel

I have a doubt here.
Since we know after combining the 2 statements that the Prime number will NOT be 3 but any other Prime number that divides at least 1 number in the sequence.
So now we know for SURE that EVERY TERM IS NOT Divisible by a particular Prime number( Which the Questions asks). 11 will also not divide all terms but few only.

SO should the Answer not be "C" ?
Please correct me.

Thankyou
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 22 Dec 2013, 07:05
Expert's post
niyantg wrote:
Bunuel wrote:
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.


No, B is not correct. It's straight E: if p=3 then every term in S is divisible by p but if p=11 then some terms in S are divisible by p (for example 99 and 9999) and some are not (for example 9 and 999). Not sufficient.

Answer: E.

hope it's clear.


Hello Bunuel

I have a doubt here.
Since we know after combining the 2 statements that the Prime number will NOT be 3 but any other Prime number that divides at least 1 number in the sequence.
So now we know for SURE that EVERY TERM IS NOT Divisible by a particular Prime number( Which the Questions asks). 11 will also not divide all terms but few only.

SO should the Answer not be "C" ?
Please correct me.

Thankyou

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Why cannot p be 3?
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 23 Dec 2013, 06:03
niyantg wrote:
Bunuel wrote:
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.


No, B is not correct. It's straight E: if p=3 then every term in S is divisible by p but if p=11 then some terms in S are divisible by p (for example 99 and 9999) and some are not (for example 9 and 999). Not sufficient.

Answer: E.

hope it's clear.


Hello Bunuel

I have a doubt here.
Since we know after combining the 2 statements that the Prime number will NOT be 3 but any other Prime number that divides at least 1 number in the sequence.
So now we know for SURE that EVERY TERM IS NOT Divisible by a particular Prime number( Which the Questions asks). 11 will also not divide all terms but few only.

SO should the Answer not be "C" ?
Please correct me.

Thankyou



Actually question is asking , is every term in S divisible by the prime number p?

S1: p is greater than 2..Means wat? it means p cud b 3 ,5,7,11. If we say 3 then ans will be yes, Bt if we say 5 then we say no. Thats why Insufficient.

S2: at least one term is divisible by p. so ans wud b 3 or 11. 3 wud be divisible by every term of S, Bt 11 cud not be divisible by first term 9, and 999 etc.

Take both statement togather. still we cant give the ans, because p cud b 3 or 11.
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

Please advise.


Hi All,
Can any of the moderators amend this post to create a gap between the question and the query posted by morya003?
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 21 Jun 2014, 04:05
Expert's post
neo656 wrote:
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.

I think with statement 2 - if P is 3 then all the terms in the sequence are divisible by P
So my answer is B

Please advise.


Hi All,
Can any of the moderators amend this post to create a gap between the question and the query posted by morya003?

______________
Done. Thank you.
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 20 Feb 2016, 23:28
The only prime that divides all terms in the sequence: 9, 99, 999,.. is 3. So the question is essentially asking: is p=3?
(1) p can be any prime number greater than 2, hence not sufficient.
(2) p can be 3 or 11, hence not sufficient.
Both taken together, again insufficient to identify p as 3.

Answer: E

boomtangboy summarizes aptly that the question tends to prey on the mistake that the test taker will consider 3 as the only possible value from statement (2).
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 09 Mar 2016, 04:50
Here we can choose 11 and 3 as test cases and we will get E answer fairly easily
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1 [#permalink]

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New post 16 Jul 2016, 00:23
morya003 wrote:
If S is the infinite sequence: S1=9, S2=99, S3=999, ..., SK = 10^K-1, ..., is every term in S divisible by the prime number p?

(1) p is greater than 2.

(2) At least one term in sequence S is divisible by p.


From question stem we know S={9,99,999,9999,99999,999999...................99999999999999....}
We can easily eye ball that this is divisible by either 3 or 11 or a combination of their multiples.

(1) p is greater than 2.
Insufficient :- p can be 3 or 5 or 7 or 11 or 13
In some cases p divides ; in some cases it don't

(2) At least one term in sequence S is divisible by p.
Insufficient again
starting from the second term (99) all terms are divisible by either 3 and 11
But the first team 9 is divisible only by 3 and not by 11

So we cannot for sure whether the prime p that the question stem is referring to is 3 or 11.

BOTH STATEMENT INSUFFICIENT
ANSWER IS E
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Re: If S is the infinite sequence S1=9 S2=99 S3=999 SK=10^k-1   [#permalink] 16 Jul 2016, 00:23
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