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# How many integers are there between, but not including

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How many integers are there between, but not including [#permalink]

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20 Mar 2012, 00:19
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How many integers are there between, but not including, integers r and s ?

(1) s – r = 10
(2) There are 9 integers between, but not including, r + 1 and s + 1.

I may have mistakenly chosen the wrong answer, but nevertheless some expert explanation will help me understand this better.
[Reveal] Spoiler: OA
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Re: How many integers are there between, but not including [#permalink]

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20 Mar 2012, 00:38
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Hope it's clear.
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Re: How many integers are there between, but not including [#permalink]

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21 Mar 2012, 17:42
nice explanation!
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Re: How many integers are there between, but not including [#permalink]

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23 Mar 2012, 03:12
number of integers including s and r = s-r+1. Number of integers excluding s and r = s-r+1-2 = s-r-1.

1) gives us s-r-1 = 9. Sufficient
2) The number of integers between s and r will be the same as number of integers between s+1 and r+1 = 9 .Sufficient.

Hence D
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Re: How many integers are there between, but not including [#permalink]

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05 Sep 2012, 04:41
I might be wrong, but I think the second part of statement 2) : "not including r+1 and s+1" is useless since it does not change anything to the distance the two values are apart.

At least this is how I got D.
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Re: How many integers are there between, but not including [#permalink]

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05 Sep 2012, 05:07
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highdiving wrote:
I might be wrong, but I think the second part of statement 2) : "not including r+1 and s+1" is useless since it does not change anything to the distance the two values are apart.

At least this is how I got D.

If we were not told that, then yes the statement would still be sufficient, but in this case the two statements would contradict each other: answer from (1) would be 9, and the answer from (2) would be 7.

Note that: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.
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Re: How many integers are there between, but not including [#permalink]

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05 Sep 2012, 05:39
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I must be missing something and I am sorry to bother you: but why would I even need to consider s+1 when I am looking for numbers between them? Maybe Im just assuming s is the upper end and so on.

Thank you for your time and patience.

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Re: How many integers are there between, but not including [#permalink]

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27 Feb 2013, 23:16
THERE ARE og question which ask about the number of even interger between 2 numbers. This is more cheating.
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Re: How many integers are there between, but not including [#permalink]

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27 Feb 2013, 23:36
In general number of integeres when extreme numbers are omiitted is s-r-1 .

A. Since s-r=10, so answer is 9, hence A is fine
B. Again difference b/w r+1 & s+1 is s-r-1, so B is also is fiine.

so D .
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Re: How many integers are there between, but not including [#permalink]

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31 Mar 2013, 05:40
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Hope it's clear.

Hi Bunuel , if i am not mistaken , why are we assuming that r and s belongs to an evenly spaced set of integers ??
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Re: How many integers are there between, but not including [#permalink]

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31 Mar 2013, 07:21
yezz wrote:
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Hope it's clear.

Hi Bunuel , if i am not mistaken , why are we assuming that r and s belongs to an evenly spaced set of integers ??

Not sure I understand what you mean.

s and r are just two integers. The question asks: how many integers are there between, but not including r and s.

Ask yourself, how many integers are there between, but not including, 0 and 10? The answer is 9: 1, 2, 3, 4, 5, 6, 7, 8, and 9.
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Re: How many integers are there between, but not including [#permalink]

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22 May 2013, 03:51
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Hope it's clear.

But, Bunuel - Considering your example in the first case in which r=0 and s=10, the number of integers between them could be maximum 9 or it could be any number less than that. Because, there is no mention of the word "consecutive" in the question. But, the second one clearly states that there are 9 integers. Hence B is sufficient, but A is not! Can you please explain where I am going wrong? Since this is an official problem and also you had solved it, I am 100% confident that D is the answer, but, I want to know where I am going wrong.
Thanks!
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Re: How many integers are there between, but not including [#permalink]

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22 May 2013, 03:57
sharmila79 wrote:
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Hope it's clear.

But, Bunuel - Considering your example in the first case in which r=0 and s=10, the number of integers between them could be maximum 9 or it could be any number less than that. Because, there is no mention of the word "consecutive" in the question. But, the second one clearly states that there are 9 integers. Hence B is sufficient, but A is not! Can you please explain where I am going wrong? Since this is an official problem and also you had solved it, I am 100% confident that D is the answer, but, I want to know where I am going wrong.
Thanks!

You don't need the word "consecutive".

How many integers are there between, but not including 1 and 3? Only one integer: 2.
How many integers are there between, but not including 1 and 5? Three: 2, 3, and 4.

Similarly: how many integers are there between, but not including, 0 and 10? The answer is 9: 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Hope it's clear.
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Re: How many integers are there between, but not including [#permalink]

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22 May 2013, 09:39
Bunuel wrote:
sharmila79 wrote:
Bunuel wrote:
How many integers are there between, but not including, integers r and s ?

Notice that we are told that r and s are integers.

(1) s – r = 10 --> since r and s are integers and s – r = 10 then there will be 9 integers between them. For example take s=10 and r=0, then there are following integers between them: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Sufficient.

(2) There are 9 integers between, but not including, r + 1 and s + 1 --> the distance between r and s is the same as the distance between r+1 and s+1, so if there are 9 integers between, but not including, r+1 and s+1 then there will be 9 integers between, but not including, r and s too. For example consider s+1=11 and r+1=1 (9 integers between them: 2, 3, 4, 5, 6, 7, 8, 9, and 10) --> s=10 and r=0 the same as above. Sufficient.

Hope it's clear.

But, Bunuel - Considering your example in the first case in which r=0 and s=10, the number of integers between them could be maximum 9 or it could be any number less than that. Because, there is no mention of the word "consecutive" in the question. But, the second one clearly states that there are 9 integers. Hence B is sufficient, but A is not! Can you please explain where I am going wrong? Since this is an official problem and also you had solved it, I am 100% confident that D is the answer, but, I want to know where I am going wrong.
Thanks!

You don't need the word "consecutive".

How many integers are there between, but not including 1 and 3? Only one integer: 2.
How many integers are there between, but not including 1 and 5? Three: 2, 3, and 4.

Similarly: how many integers are there between, but not including, 0 and 10? The answer is 9: 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Hope it's clear.

GMAT questions are tricky and they demand over- cautiousness! This is one such occasion...
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Re: How many integers are there between, but not including [#permalink]

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27 Jan 2015, 08:09
Bunuel , why can't s and r be negative?s could be -10 and r could be 20 so s-r would still be 10 but the number of integers would be 30?I'm sure i'm missing something stupid here.
:/
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Re: How many integers are there between, but not including [#permalink]

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27 Jan 2015, 08:11
Ralphcuisak wrote:
Bunuel , why can't s and r be negative?s could be -10 and r could be 20 so s-r would still be 10 but the number of integers would be 30?I'm sure i'm missing something stupid here.
:/

If s = -10 and r = 20, then s - r = -10 - 20 = -30, not 10.
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Re: How many integers are there between, but not including [#permalink]

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27 Jan 2015, 10:08
Oh.i knew its something stupid.This warrants a break.Thanks a ton Bunuel . You rock.
Re: How many integers are there between, but not including   [#permalink] 27 Jan 2015, 10:08
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