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How many integers n are there such that r < n < s ?
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29 Sep 2010, 06:05
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How many integers n are there such that r < n < s ?
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29 Sep 2010, 06:18
SOLUTIONHow many integers n are there such that r < n< s ?The question asks: how many integers \(n\) satisfy \(r < n < s\), or how many integers are between \(r\) and \(s\), not inclusive? Notice that if \(r\) and \(s\) are integers, for example \(s=5\) and \(r=0\) then there will be 4 integers between them: 1, 2, 3, and 4. But if \(r\) and \(s\) are NOT integers for example \(s=5.5\) and \(r=0.5\) then there will be 5, so one more, integers between them: 1, 2, 3, 4 and 5. (1) s  r = 5. Not sufficient. (2) r and s are not integers. Not sufficient. (1)+(2) According to above reasoning since r and s are not integers then there are 5 integers between them (case 2). Sufficient. Answer: C. Similar questions to practice: http://gmatclub.com/forum/howmanyinte ... 15561.htmlhttp://gmatclub.com/forum/howmanyinte ... 29065.html
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Re: How many integers n are there such that r < n < s ?
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29 Sep 2010, 08:42
The "number" of n can be multiple of 4 or 5, says 8 or 10, 12, 15, ... can not be determined...



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Re: How many integers n are there such that r < n < s ?
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29 Sep 2010, 08:56
ezinis wrote: The "number" of n can be multiple of 4 or 5, says 8 or 10, 12, 15, ... can not be determined... It seems that you misinterpreted the question. Question ask about the number of integers between r and s, not inclusive. For example: how many integers are between 10 and 15, not inclusive? Answer: 4, namely 11, 12, 13, and 14. Or: how many integers are between 5.3 and 10.3? Answer: 5, namely 5, 6, 7, 8, 9 and 10. So taken together statements are sufficient to answer that there are 5 integers between r and s. Hope it's clear.
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Re: How many integers n are there such that r < n < s ?
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22 Apr 2012, 13:09
Bunuel wrote: How many integers n are there such that r < n< s ?
The question asks: how many integers \(n\) satisfy \(r < n < s\), or how many integers are between \(r\) and \(s\), not inclusive?
Notice that if \(r\) and \(s\) are integers, for example \(s=5\) and \(r=0\) then there will be 4 integers between them: 1, 2, 3, and 4. But if \(r\) and \(s\) are NOT integers for example \(s=5.5\) and \(r=0.5\) then there will be 5, so one more, integers between them: 1, 2, 3, 4 and 5.
(1) s  r = 5. Not sufficient. (2) r and s are not integers. Not sufficient.
(1)+(2) According to above reasoning since r and s are not integers then there are 5 integers between them (case 2). Sufficient.
Answer: C.
Hope it's clear. can you please eleborate the concept behind this ?? indeed is true but I didn't notice this before. Thanks
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Re: How many integers n are there such that r < n < s ?
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22 Apr 2012, 13:15
carcass wrote: Bunuel wrote: How many integers n are there such that r < n< s ?
The question asks: how many integers \(n\) satisfy \(r < n < s\), or how many integers are between \(r\) and \(s\), not inclusive?
Notice that if \(r\) and \(s\) are integers, for example \(s=5\) and \(r=0\) then there will be 4 integers between them: 1, 2, 3, and 4. But if \(r\) and \(s\) are NOT integers for example \(s=5.5\) and \(r=0.5\) then there will be 5, so one more, integers between them: 1, 2, 3, 4 and 5.
(1) s  r = 5. Not sufficient. (2) r and s are not integers. Not sufficient.
(1)+(2) According to above reasoning since r and s are not integers then there are 5 integers between them (case 2). Sufficient.
Answer: C.
Hope it's clear. can you please eleborate the concept behind this ?? indeed is true but I didn't notice this before. Thanks There isn't some special concept behind it. It's just common sense based on observation.
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Re: How many integers n are there such that r < n < s ?
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18 Jun 2013, 19:35
I had and still continue to have trouble interpreting this question.
how many integers n are there such that r<n<s r and s are 0 or 5 > n can be 1,2,3,4 r and s are 110 or 115> n can be another set of 4 no.s
i thought n can have any number of infinite values for rs=5 or for r and s are not integers.....can some one pls make it clear...
i understand some of the explanations are towards n=no. of integers between two given values, but question ask how many integers n are there that meet the criteria...



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Re: How many integers n are there such that r < n < s ?
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19 Jun 2013, 01:36



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Re: How many integers n are there such that r < n < s ?
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21 Jan 2014, 07:31
Imp. Point its given n is integer not r and s. So we can assume them to be integer .
Possibility 1  r and s are integer s=10, r=5 n can be 6,7,8,9
Possibility 2  r and s are not integer s=9.9, r=4.9 n can be 5,6,7,8,9
Condition 1 : sr =5 (not sufficient by logic above)
Condition 2 : r and s are noninteger (not sufficient)
Combine 1 and 2 and value of n will be 5 always.
so answer is (C)



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Re: How many integers n are there such that r < n < s ?
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24 Jan 2014, 00:10
(1) s  r = 5 let s= 6.5 and r=1.5 then there are 5 integers between s and r , 2,3,4,5 and 6. let s=6 and r=1 then there are 4 integers between s and r, 2,3,4, and 5 hence insufficient (2) r and s are not integers. Clearly insufficient s=10.5 r=1.5 or s=2.5 r=1.5, etc 1+2 Sufficient as any 2 non integers , such that their difference is 5, will have 5 integers between them. e.g. s= 6.5 and r=1.5 then there are 5 integers between s and r , 2,3,4,5 and 6 Answer C
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Re: How many integers n are there such that r < n < s ?
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18 May 2014, 09:46
if we knew about s and r (integers or not integers) our task would be simplified to st(1) Suff. Since we know nothing about s and r, there could be always four integers (case when s and r are integers) or five integers (when s or r is not integer)
st(2) helps with assigning type for our numbers (s and r), but we know nothing about values
combined st(1&2) supports our previously inquired data, i.e. s and r are not integers, hence the number of integers in the given interval will always be 5.
answer c)



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Re: How many integers n are there such that r < n < s ?
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06 Nov 2018, 08:53
Bunuel wrote: How many integers n are there such that r < n < s ? (1) s  r = 5 (2) r and s are not integers. Data Sufficiency Question: 49 Category: Arithmetic Properties of numbers Page: 156 Difficulty: 650 The Official Guide For GMAT® Quantitative Review, 2ND Editions  r = 5 If s = 6 and r = 1 then 1 < n < 6 so n can be 5,4,3,2. I almost fell trap for picking an integer but luckily the second statement made me consider the option of fractions. if s = 21/2 and n = 11/2 then 5.5 < n < 10.5 so n can be 10,9,8,7,6 (5 integers) Insufficient. Statement 2 tells us that s and r are not integers. We already tested one case above so we try another one. s = 3/2 and r = 1/6 1/6 < n < 1.5 then n can be 1 (1 integer) Insufficient. Combined we get they are not integers and they subtract to 5 21/2 11/2 = 5 and gives us that n has 5 integers that satisfy the equation. This can also be the case if we test 21/4  1/4 = 20/4 = 5 0.25 < n < 5.25 how many possible integers? (5,4,3,2,1) total 5. Sufficient. C is the answer choice



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Re: How many integers n are there such that r < n < s ?
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06 Nov 2018, 17:59
Bunuel wrote: nanz236 wrote: I had and still continue to have trouble interpreting this question.
how many integers n are there such that r<n<s r and s are 0 or 5 > n can be 1,2,3,4 r and s are 110 or 115> n can be another set of 4 no.s
i thought n can have any number of infinite values for rs=5 or for r and s are not integers.....can some one pls make it clear...
i understand some of the explanations are towards n=no. of integers between two given values, but question ask how many integers n are there that meet the criteria... How many integers n are there such that 0 < n < 5? Answer: 4. How many integers n are there such that 110 < n < 115? Answer: 4. Does this make sense? Excuse me, Bunuel, why in this case you haven't considered negatives? Thank you.



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How many integers n are there such that r < n < s ?
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22 Dec 2018, 13:43
How many integers n are there such that r < n < s ?
(1) s  r = 5 (2) r and s are not integers.
Let's say we consider negative values like you suggested for r < n < s => possible values for s  r = 5 would be s=4 and r = 1 or s=3 and r=2 ...
2 < n < 3 => 2 < 1 < 0 < 1 < 2 < 3 => 4 integers
The only condition where you have 5 integers is when you have fractions =>
2.5 < n < 2.5 => 2.5 < 2 < 1 < 0 < 1 < 2 < 2.5 => 5 integers
You will need to use condition 2 to eliminate the fractions. Hence C




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