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In the infinite sequence S, where S1 = 25, S2 = 125, S3 =

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In the infinite sequence S, where S1 = 25, S2 = 125, S3 = [#permalink] New post   19 Jun 2011, 08:03
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In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.
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Re: Series based D.S Problem [#permalink] New post   06 Sep 2011, 22:28
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guygmat wrote:
In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.


The given sequence: 25, 125, 225, 325, 425 ...
x is an odd integer.
Question: Is x a divisor of every member of S?

(1) x is a divisor of every member starting from third term i.e. x is a divisor of 225, 325, 425 etc. Note here that the statement doesn't say that x is not a divisor of first two terms. It just says that it definitely is the divisor of every term starting from 3rd term.
Let's take 2 of these terms:
225 = 25*9
325 = 25*13
Note here that if x is an odd divisor of both these numbers, x must be 1/5/25. Those are the only common divisors that these two terms have.
If x is one of 1, 5 and 25, it is the divisor of every term in the sequence since every term is divisible by each of these three numbers. Sufficient.

2) x is a divisor of 500
Odd divisors of 500: 1, 5, 25, 125
If x is one of 1, 5 and 25, it is the divisor of every term in the sequence since every term is divisible by each of these three numbers.
If x = 125, it is not a divisor of the first term i.e. 25
Since x may or may not be the divisor of every term, this statement alone is not sufficient.

Answer (A)
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sudhir18n
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Re: Series based D.S Problem [#permalink] New post   19 Jun 2011, 08:17
guygmat wrote:
In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.


can some one explain this ?
i thought both 5 and 25 can be the factors/divisors..
by any chance is the question asking us if X is an odd integer? irrespective of the value of X ( 5,25 both are odd)
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Re: Series based D.S Problem [#permalink] New post   20 Jun 2011, 07:52
sudhir18n wrote:
guygmat wrote:
In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.


can some one explain this ?
i thought both 5 and 25 can be the factors/divisors..
by any chance is the question asking us if X is an odd integer? irrespective of the value of X ( 5,25 both are odd)


Stem is telling us that "x is an odd integer"
And then it asks;
Is it a factor of all the elements in the series.

Good question guygmat.
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Re: Series based D.S Problem [#permalink] New post   06 Sep 2011, 03:44
Quote:
In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.


From Statement 1
x is not a divisor for S1 and S2 ---> i.e. x is not a divisor of every member of S.
Sufficient

From Statement 2
prime factors of 500: 5, 2, 5, 2, 5
x can be 5 or 2.
Insufficient.

Answer: A
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Re: Series based D.S Problem [#permalink] New post   06 Sep 2011, 11:18
gmatopoeia wrote:
Quote:
In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.


From Statement 1
x is not a divisor for S1 and S2 ---> i.e. x is not a divisor of every member of S.
Sufficient

From Statement 2
prime factors of 500: 5, 2, 5, 2, 5
x can be 5 or 2.
Insufficient.

Answer: A


Actually, I say the opposite for statement 1.
x is [strike]not[/strike] a divisor for S1 and S2.---> i.e. x is [strike]not[/strike] a divisor of every member of S.
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Re: Series based D.S Problem [#permalink] New post   06 Sep 2011, 14:38
Quote:

fluke wrote:


Quote:

gmatopoeia wrote:



In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.


From Statement 1
x is not a divisor for S1 and S2 ---> i.e. x is not a divisor of every member of S.
Sufficient

From Statement 2
prime factors of 500: 5, 2, 5, 2, 5
x can be 5 or 2.
Insufficient.

Answer: A



Actually, I say the opposite for statement 1.
x is [strike]not[/strike] a divisor for S1 and S2.---> i.e. x is [strike]not[/strike] a divisor of every member of S.


Sorry Fluke, could you explain why you say so?

How I understood it is:
In statement one, it says x is a divisor of Sk only for values whereby k≥3. So, when k=1(i.e. S1) and k=2 (i.e. S2), x is not a divisor of S. That's how I came to say: x is not a divisor for S1 and S2.---> i.e. x is not a divisor of every member of S.

pls let me know if you see a flaw in my reasoning..
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Re: Series based D.S Problem [#permalink] New post   06 Sep 2011, 23:27
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VeritasPrepKarishma wrote:
The given sequence: 25, 125, 225, 325, 425 ...
x is an odd integer.
Question: Is x a divisor of every member of S?

(1) x is a divisor of every member starting from third term i.e. x is a divisor of 225, 325, 425 etc. Note here that the statement doesn't say that x is not a divisor of first two terms. It just says that it definitely is the divisor of every term starting from 3rd term.
Let's take 2 of these terms:
225 = 25*9
325 = 25*13
Note here that if x is an odd divisor of both these numbers, x must be 1/5/25. Those are the only common divisors that these two terms have.
If x is one of 1, 5 and 25, it is the divisor of every term in the sequence since every term is divisible by each of these three numbers. Sufficient.


Precisely that was my reasoning. thanks Karishma.
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Re: Series based D.S Problem [#permalink] New post   07 Sep 2011, 01:03
Quote:

VeritasPrepKarishma wrote:



Quote:

guygmat wrote:


In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.



The given sequence: 25, 125, 225, 325, 425 ...
x is an odd integer.
Question: Is x a divisor of every member of S?

(1) x is a divisor of every member starting from third term i.e. x is a divisor of 225, 325, 425 etc. Note here that the statement doesn't say that x is not a divisor of first two terms. It just says that it definitely is the divisor of every term starting from 3rd term.
Let's take 2 of these terms:
225 = 25*9
325 = 25*13
Note here that if x is an odd divisor of both these numbers, x must be 1/5/25. Those are the only common divisors that these two terms have.
If x is one of 1, 5 and 25, it is the divisor of every term in the sequence since every term is divisible by each of these three numbers. Sufficient.

2) x is a divisor of 500
Odd divisors of 500: 1, 5, 25, 125
If x is one of 1, 5 and 25, it is the divisor of every term in the sequence since every term is divisible by each of these three numbers.
If x = 125, it is not a divisor of the first term i.e. 25
Since x may or may not be the divisor of every term, this statement alone is not sufficient.

Answer (A)


oh! I really would never have seen it that way if not for your explanation...thanks, Karishma! The same goes for statement 2 - I missed the detail in the stem that x is odd. Looks like my getting the question right was a fluke (no pun intended!) ... :-D
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Re: Series based D.S Problem [#permalink] New post   07 Sep 2011, 07:28
VeritasPrepKarishma wrote:
guygmat wrote:
In the infinite sequence S, where S1 = 25, S2 = 125, S3 = 225, ..., Sk = 100*(k-1) + 25, is odd integer x a divisor of every member of S?

(1) For all values of k ≥ 3, x is a divisor of Sk.

(2) x is a divisor of 500.


The given sequence: 25, 125, 225, 325, 425 ...
x is an odd integer.
Question: Is x a divisor of every member of S?

(1) x is a divisor of every member starting from third term i.e. x is a divisor of 225, 325, 425 etc. Note here that the statement doesn't say that x is not a divisor of first two terms. It just says that it definitely is the divisor of every term starting from 3rd term.
Let's take 2 of these terms:
225 = 25*9
325 = 25*13
Note here that if x is an odd divisor of both these numbers, x must be 1/5/25. Those are the only common divisors that these two terms have.
If x is one of 1, 5 and 25, it is the divisor of every term in the sequence since every term is divisible by each of these three numbers. Sufficient.

2) x is a divisor of 500
Odd divisors of 500: 1, 5, 25, 125
If x is one of 1, 5 and 25, it is the divisor of every term in the sequence since every term is divisible by each of these three numbers.
If x = 125, it is not a divisor of the first term i.e. 25
Since x may or may not be the divisor of every term, this statement alone is not sufficient.

Answer (A)


Hi, ur explanation was good thanks!.
can you plz tell me the difference between
x is a divisor of 500 and x is a divides 500
x is a divisor of 500 means multiples of 500?
x is a divides 500 means x/500 =0?
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Re: Series based D.S Problem [#permalink] New post   07 Sep 2011, 07:54
Quote:

ssruthi wrote:


Hi, ur explanation was good thanks!.
can you plz tell me the difference between
x is a divisor of 500 and x is a divides 500
x is a divisor of 500 means multiples of 500?
x is a divides 500 means x/500 =0?


x is a divisor of 500 means all of the below:
1. x multiplied by another number gives you 500,
2. x is a factor of 500, and
3. 500 is a multiple of x

hope that helps! :-D
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Re: In the infinite sequence S, where S1 = 25, S2 = 125, S3 = [#permalink] New post   08 Jun 2019, 06:36
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Re: In the infinite sequence S, where S1 = 25, S2 = 125, S3 = [#permalink]
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