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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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15 Oct 2012, 04:51
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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.

Practice Questions
Question: 64
Page: 280
Difficulty: 600
[Reveal] Spoiler: OA

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

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15 Oct 2012, 04:51
Expert's post
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SOLUTION

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.

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

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15 Oct 2012, 05:06
1
KUDOS
The best way to solve such kind of problem is to use Number line (Sorry i am not including the same)
1) Two integers are 10 units apart, thus the no of integers between 2 integers will be 9---->Sufficient
2) The no of integers between 2 integers r+1 & s+1 is 9. If we move 1 unit in the same direction, no of integers will remain same, which will be 9--->Sufficient

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

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16 Oct 2012, 05:37
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statement 1

s=r+10

so basically the numbers we have are r,r+1,r+2,r+3,r+4,r+5,r+6,r+7,r+8,r+9,r+10( r+10 is S)

so there are 9 integers in between another way to solve would be s-r+1 = 10+1 = 11 total number of integers
since we need the numbers in between 11 - 2 ( the 2 numbers we subtract are r and s) hence we get 9

statement 2

there are 9 integers so we have a total of 11 integers at the moment.

s+1 - (r+1) + 1 = 11
s+1-r-1=10
s-r=10 which is same as statement 1 sufficient

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

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16 Oct 2012, 06:10
1
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From statement 1,
s-r=10
Sufficient to conclude number that s is 9 integers after r.

Statment 2,
s+1 is 9 integers after r+1
or s is 9 integers after r (same as S1)
Sufficient.

Hence D

Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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.

Practice Questions
Question: 64
Page: 280
Difficulty: 600

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

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19 Oct 2012, 05:34
SOLUTION

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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: How many integers are there between, but not including [#permalink]

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21 Jan 2013, 18:57
Bunuel wrote:
SOLUTION

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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.

I still do not understand how (1) is sufficient. My train of thought on it being insufficient is as follows with and example
s-r=10

12-2= 10 if s= 12 and r= 2 but the consecutive set could be consecutive multiples 2,4,6,8,10,12. There would only be 4 integer in between.
Do we just assume they are a consecutive set of integers?
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Re: How many integers are there between, but not including [#permalink]

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22 Jan 2013, 04:40
inportsmouthva wrote:
Bunuel wrote:
SOLUTION

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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.

I still do not understand how (1) is sufficient. My train of thought on it being insufficient is as follows with and example
s-r=10

12-2= 10 if s= 12 and r= 2 but the consecutive set could be consecutive multiples 2,4,6,8,10,12. There would only be 4 integer in between.
Do we just assume they are a consecutive set of integers?

Let me ask you a question: how many integers are there between, but not including, 2 and 12?
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Re: How many integers are there between, but not including [#permalink]

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22 Jan 2013, 06:34
Bunuel wrote:

Let me ask you a question: how many integers are there between, but not including, 2 and 12?

BINGO- I get it now. The lights just went on. There are 9. The question specifically states how many integers between the two numbers. It does not mention intervals. The question states "integers between"
The good thing is that I am learning that I am sometimes reading way too much into a question, thinking it can not be this easy.
This is part of my learning "what to watch out for, and what kind of mistakes I am making"
Thanks so much for your help
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Re: How many integers are there between, but not including [#permalink]

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24 Jan 2013, 04:14
its a sub 600 level question
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Re: How many integers are there between, but not including [#permalink]

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01 Jul 2014, 20:32
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Re: How many integers are there between, but not including [#permalink]

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26 Jul 2015, 04:35
The number of integers between two numbers r and s (including both numbers) is s - r +1
The number of integers between two numbers r and s (excluding both numbers) is s - r - 1

Basically the question is asking the value of (s - r - 1)?

(1) s - r = 10.
10 - 1 = 9 Sufficient

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

[(s + 1) - (r + 1) - 1] = 9
or (s - r - 1 ) = 9 Sufficient

Hence D.
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Re: How many integers are there between, but not including   [#permalink] 26 Jul 2015, 04:35
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