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The sequence is defined as follows: A(n) = n/(n+1).

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The sequence is defined as follows: A(n) = n/(n+1).  [#permalink] New post 01 Aug 2007, 07:25
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The sequence is defined as follows:

A(n) = n/(n+1).

How many of the first 100 terms of this sequence are less than 0.891

A) 7
B) 8
C) 9
D)10
E) 12
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Re: PS Sequences [#permalink] New post 01 Aug 2007, 07:58
raptr wrote:
The sequence is defined as follows:

A(n) = n/(n+1).

How many of the first 100 terms of this sequence are less than 0.891

A) 7
B) 8
C) 9
D)10
E) 12


It is B.

A(9) = 0.9
A(8) = 0.89

Therefore, 8 terms are less than 0.891.
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 [#permalink] New post 01 Aug 2007, 08:08
i used brute force method to arrive at the numbers

1/2 , 2/3, 3/4, 4/5, 5/6 , 6/7 , 7/8, 8/9

all these are less than 0.891 .. others that follow inthis series are greater than 0.891. Hence B i.e 8 is the answer
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 [#permalink] New post 01 Aug 2007, 09:38
OA is B) 8.

What I don't understand is how do you decide which term exactly is "the first term" and why [b]n[/b] can't be 0 or negative.

If n=0 -> n/n+1 = 0/1 = 0 and 0<0.891
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 [#permalink] New post 01 Aug 2007, 09:47
raptr wrote:
OA is B) 8.

What I don't understand is how do you decide which term exactly is "the first term" and why n can't be 0 or negative.

If n=0 -> n/n+1 = 0/1 = 0 and 0<0.891


That question did pop in my mind.
For n=-1, A(n) is undefined. For all other negative values of n, A(n) will be greater than 1. So, even considering negative integers won't make much of a difference.

But as you rightly pointed out, n=0 does make a difference. Further the question does not even mention that n is an integer !!

All in all, I believe that it is not a very well constructed question (if, of course, you have copied down the question completely ). Any other opinions ?? :-D
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 [#permalink] New post 01 Aug 2007, 10:31
No, it cant be B...cause we are not told if N is positive and greater than 0 or not..cause 0/1=0 which is less than 0.89 and thus the number should be 9...

I would say not knowing if N is positive and greater than 0...the number is 9 not 8...

any takers??
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Re: PS Sequences [#permalink] New post 01 Aug 2007, 11:07
raptr wrote:
The sequence is defined as follows:

A(n) = n/(n+1).

How many of the first 100 terms of this sequence are less than 0.891

A) 7
B) 8
C) 9
D)10
E) 12


I initially looked at B) 8, but after looking for the typical GMAT traps, I tried A(0) ~ I think it should be C) 9 as well. In the GMAT, x/0 is undefined, but 0/x is not. right?
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 [#permalink] New post 01 Aug 2007, 12:09
0/x i definitely not undefined. I picked "C" and it turned out to be the wrong answer. I tought I am missing something fundamental... obviously I am not. Or am I?

I copied the problem word for word. This is the explanation:

"Let's write out first 10 terms of this series: 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11. Any subsequent element in this series is bigger than its predecessor. To answer the question we have to find the first element that is bigger than 0.891. It is the 9th element = 9/10 = 0.900; 8/9 = 0.888... is less than 0.891. Thus, there are only 8 elements in the whole series that are less than 0.891. "

As you can see, it doesn't consider n<1.

I have no explanation. The official answer is B) This is question #3 from Challenge #14.

->>> I am not aware of a rule against posting Challenge materials here, but if there is such a rule and I am violating it, I appologize.
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 [#permalink] New post 01 Aug 2007, 12:19
raptr wrote:
0/x i definitely not undefined. I picked "C" and it turned out to be the wrong answer. I tought I am missing something fundamental... obviously I am not. Or am I?

I copied the problem word for word. This is the explanation:

"Let's write out first 10 terms of this series: 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11. Any subsequent element in this series is bigger than its predecessor. To answer the question we have to find the first element that is bigger than 0.891. It is the 9th element = 9/10 = 0.900; 8/9 = 0.888... is less than 0.891. Thus, there are only 8 elements in the whole series that are less than 0.891. "

As you can see, it doesn't consider n<1>>> I am not aware of a rule against posting Challenge materials here, but if there is such a rule and I am violating it, I appologize.


there is a rule, but don't worry... I had many problems with the challenges
as some of the answers/explanations are 'iffy'. I chose B - but everyone's objections are valid. I checked the GMAT OG math rules... it says the domain of a function can consist of only positive values and possible zero (not sure why we can't have negative values for a domain?)

so in this problem, i think unless the domain is restricted to positive values that answer is technically 9
  [#permalink] 01 Aug 2007, 12:19
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