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How many integers are there between, but not including
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15 Oct 2012, 04:51
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Re: How many integers are there between, but not including
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15 Oct 2012, 04:51
SOLUTIONHow 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. Answer: D.
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Re: How many integers are there between, but not including
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15 Oct 2012, 05:06
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 Answer D
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Re: How many integers are there between, but not including
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16 Oct 2012, 05:37
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 sr+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+1r1=10 sr=10 which is same as statement 1 sufficient
so answer is D



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Re: How many integers are there between, but not including
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16 Oct 2012, 06:10
From statement 1, sr=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 ProjectHow many integers are there between, but not including, integers r and s ? (1) sr=10 (2) There are 9 integers between, but not including, r + 1 and s + 1. Practice Questions Question: 64 Page: 280 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a solution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: How many integers are there between, but not including
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19 Oct 2012, 05:34
SOLUTIONHow 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. Answer: D. 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
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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.
Answer: D.
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 sr=10 122= 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
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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.
Answer: D.
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 sr=10 122= 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
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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
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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
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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
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04 Feb 2017, 01:03
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.
Answer: D. Hi Bunuel, how to know that the integers between r and s are consecutive integers?



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Re: How many integers are there between, but not including
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04 Feb 2017, 01:06
Kchaudhary 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.
Answer: D. Hi Bunuel, how to know that the integers between r and s are consecutive integers? Integers between r and s consists of all the integers between r and s, so they ARE consecutive. For example, integers between 5 and 10 are 6, 7, 8, and 9, which are naturally consecutive.
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Re: How many integers are there between, but not including
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12 Apr 2018, 19:26
one small doubt in the statement 1. Why shouldn't we consider s=10 and r=20 in which case the sum is 10 but the number of integers between them is not 9. Kindly explain



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Re: How many integers are there between, but not including
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Re: How many integers are there between, but not including
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12 Apr 2018, 21:23
How many integers are there between, but not including, integers r and s ? (1) sr=10 S and R are integers , so if sr = 10, then there would be 9 integers between s and r. Sufficient. (2) There are 9 integers between, but not including, r + 1 and s + 1. 9 integers between but not including r+1 and s+1 , the number of integers between r+1 and s+1 is the same as number of integers between r and s. Hence Sufficient. Ans: D
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Re: How many integers are there between, but not including
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26 Apr 2018, 20:52
I) As s and r are integers so whatever be their value there would be always 9 integers be them. Eg 1 and 11 4 and 6 Sufficient II)watever be number of integers be r and s ,same would be case bw r+1 and s+1 Sufficient D Posted from my mobile device
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Re: How many integers are there between, but not including
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15 May 2018, 10:16
Why did we assume that R to S is continuous series ? can't it be 0, 1, 10
R=0, S=10 ..but number of integer between S and R will 1.



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Re: How many integers are there between, but not including
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15 May 2018, 10:49
ammuseeru wrote: Why did we assume that R to S is continuous series ? can't it be 0, 1, 10
R=0, S=10 ..but number of integer between S and R will 1. Hello What do you mean by continuous series  can you please make it clear? Whichever values we assume for r/s, as far as those values satisfy the given constraint (that s  r = 10), there will always be 9 integers between them. The values that you have taken: r=0, s=10  here also there are 9 integers between r and s (1, 2, 3, 4, 5, 6, 7, 8, 9).




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