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Sumithra
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How many integer n are there such that r<n<s? 1)s-r=5 13 Jan 2007, 12:48
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How many integer n are there such that r<n<s?

1)s-r=5

I just wanted to know how you guys would approach with just 1 statement.
Will post the second later.



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How many integer n are there such that r<n<s? 1)s-r=5 13 Jan 2007, 13:07
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Sumithra
How many integer n are there such that r<n<s?

1)s-r=5

I just wanted to know how you guys would approach with just 1 statement.
Will post the second later.
Show more


Just as you expected (my guess..:) , the first instinct was to say 5. Then I realised that cant be true and quickly checked. it turns out to be (r-s) -1.
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Fig
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How many integer n are there such that r<n<s? 1)s-r=5 13 Jan 2007, 13:08
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This is my view :)

s-r = 5 gives us the distance between s and r. We can already conclude that there are 4 values of n :)

Also, algebrically, we can rewrite the original inequations :

r<n<s
<=> r < n < r + 5 as s = 5 + r

And here, it too shows that n could have 4 values :)
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Sumithra
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How many integer n are there such that r<n<s? 1)s-r=5 13 Jan 2007, 15:15
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For those of you who would like to see the rest of the Q, OA, and OE, highlight the following.

I wanted to see if any of you would try for both integers and fractions.
Well, if you have not, then keep it in mind.

2) r and s are not integers.

OA: C

OE:From S1, it can be concluded that the no. of integers is 4 r and s are integers and the no. of integers is 5 if r and s are not integers. S2 alone is not suff since it gives no info about how far apart s and r are.

Of course, S2 gives a clue.
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How many integer n are there such that r<n<s? 1)s-r=5 13 Jan 2007, 15:20
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Sumithra
For those of you who would like to see the rest of the Q, OA, and OE, highlight the following.

I wanted to see if any of you would try for both integers and fractions.
Well, if you have not, then keep it in mind.

2) r and s are not integers.

OA: C

OE:From S1, it can be concluded that the no. of integers is 4 r and s are integers and the no. of integers is 5 if r and s are not integers. S2 alone is not suff since it gives no info about how far apart s and r are.

Of course, S2 gives a clue.
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My favorite "silly" mistake ;)... Always following in ;)... I have readen r, s and n integers... hard to go out from it :)

Well done, Sumithra :)... U show what we should not do ! :)
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How many integer n are there such that r<n<s? 1)s-r=5 13 Jan 2007, 15:33
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damn, I never learn...:) Thank goodness for statement 2.
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Sumithra
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How many integer n are there such that r<n<s? 1)s-r=5 13 Jan 2007, 15:39
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I too used the help from S2. That is why I wanted to remind others of such traps.
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How many integer n are there such that r<n<s? 1)s-r=5 14 Jan 2007, 17:54
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r and s are 5 integers apart so with 1 alone n can be 4 or 5 ( 4 when r & s are integers, 5 when they are not)
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How many integer n are there such that r<n<s? 1)s-r=5 15 Jan 2007, 19:13
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If s, r integers:
Plug in #s: r=4, s=9: numbers in between: 5, 6, 7, 8 => 4 #s.

If s, r reals not integers:
Plug in #s: r=4.1, s=9.1: #s in between: 5, 6, 7, 8 , 9 => 5 #s.
Another case: r=4.9, s=9.9: #s in between: 5, 6, 7, 8, 9 => 5 #s.

Insuff => B, C, or E.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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