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How many integers n are there such that r < n < s? (1) [#permalink]
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29 Mar 2005, 19:37
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How many integers n are there such that r < n < s?
(1) sr = 5
(2) r and s are not integers
I am having a rough time with inequalities so explanation would be highly appreciated. Thanks



VP
Joined: 25 Nov 2004
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Re: DS Inequality 3 [#permalink]
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29 Mar 2005, 19:54
from (1), s could be any integer or any number so does r. n varies with the values of s or n.
from (2), it is clear that r and s are not integers but we do not know what are the values of r and s.
from 1 and 2 only we know that there are 5 integer values for n.



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Joined: 07 Jul 2004
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1) sr=5
n will always be 4 whatever the combination of r and s
S can be 6, r can be 1, n =4
S can be 12, r can be 7, n=4
S can be 100, r can be 95, n=4
So 1 is sufficient.
2) r and s are not integers
Clearly not sufficient.
r and be 33/2 and s=39/2, then n= 3
r can be 33/2 and s=43/2, then n= 4
So A is the answer.



VP
Joined: 18 Nov 2004
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"C"...come on guys think abt this again.....it can't be "A"...where does it say r and s are integers ?



GMAT Club Legend
Joined: 07 Jul 2004
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banerjeea_98 wrote: "C"...come on guys think abt this again.....it can't be "A"...where does it say r and s are integers ?
oops.... didn't think about that part. youre right, we need to consider fractions as well.



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Here's my reworked solution. Sorry, I alway forget about integers...
1) Not sufficient. If s and r are integers, then n=4. However, if s and r are not integers, then n=5
2) r and s are not integers. Not sufficient. s and r can be sets of different values, giving no definite value for n.
1 + 2> Tells us r and s are not integers, so n=5.
Ans:C



Director
Joined: 27 Dec 2004
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ywilfred wrote: Here's my reworked solution. Sorry, I alway forget about integers... 1) Not sufficient. If s and r are integers, then n=4. However, if s and r are not integers, then n=5 2) r and s are not integers. Not sufficient. s and r can be sets of different values, giving no definite value for n. 1 + 2> Tells us r and s are not integers, so n=5. Ans:C
That's my problem too. I tend to forget about integers and non integers. There is this force in me that keeps assuming everything is an integer. arrrrrrrrrrrrrrrrrrrrrrrrggh!



VP
Joined: 18 Nov 2004
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Folaa3 wrote: ywilfred wrote: Here's my reworked solution. Sorry, I alway forget about integers... 1) Not sufficient. If s and r are integers, then n=4. However, if s and r are not integers, then n=5 2) r and s are not integers. Not sufficient. s and r can be sets of different values, giving no definite value for n. 1 + 2> Tells us r and s are not integers, so n=5. Ans:C That's my problem too. I tend to forget about integers and non integers. There is this force in me that keeps assuming everything is an integer. arrrrrrrrrrrrrrrrrrrrrrrrggh!
"GMAT is out to trick you with integers and nonintegers ", if you keep this in back of your mind whenever you see a DS with variables then you will be better off.



Director
Joined: 27 Dec 2004
Posts: 898

Thanks Banerjeea_98 !
Thanks everryone for the explanation, the OA is C



SVP
Joined: 03 Jan 2005
Posts: 2233

Actually, if you've forgetten that r and s can be non integer when you look at (1), (2) should serve as a very good reminder for you and you should immediately realize that you need to revisit the question from the beginning.



Manager
Joined: 07 Mar 2005
Posts: 179

guys the answer should be A only,,,,,becuase it says rs=5.....
so no matter they are intgers/fractions ,,they always have 5 integers betwwen them,,,
s= 1.2,,,r=6.2 n=5
s=1.2 ,,,,r=3.8,,,,n= 5(1,0,1,2,3)
thus answer is A
_________________
i hate when people do'nt post the OA, it leaves in guessing!!!!



Intern
Joined: 15 Feb 2005
Posts: 23

Karun,
You're right that rs=5. But you seem to have overlooked the inequality.
If r and s are integers then n cannot be either of r or s. So that leaves us only 4 integers between r and s
Example:
If 0<n<5
n has only 4 possiblities 1,2,3,4
If 0.5<n<5.5
n has 5 possiblities 1,2,3,4,5
So the answer is C.










