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# How many integers n are there such that r < n < s? (1)

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Director
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How many integers n are there such that r < n < s? (1) [#permalink]  29 Mar 2005, 18:37
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How many integers n are there such that r < n < s?

(1) s-r = 5
(2) r and s are not integers

I am having a rough time with inequalities so explanation would be highly appreciated. Thanks
VP
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Re: DS Inequality 3 [#permalink]  29 Mar 2005, 18:54
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.
GMAT Club Legend
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1) s-r=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

VP
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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
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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.
GMAT Club Legend
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Here's my re-worked 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
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ywilfred wrote:
Here's my re-worked 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
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Folaa3 wrote:
ywilfred wrote:
Here's my re-worked 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 non-integers ", if you keep this in back of your mind whenever you see a DS with variables then you will be better off.
Director
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Thanks Banerjeea_98 !

Thanks everryone for the explanation, the OA is C
SVP
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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
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guys the answer should be A only,,,,,becuase it says r-s=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)

_________________

i hate when people do'nt post the OA, it leaves in guessing!!!!

Intern
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Karun,
You're right that r-s=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

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