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s and r are positive integers, is either r or s a prime? 1)

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sparky
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s and r are positive integers, is either r or s a prime? 1) [#permalink] New post   31 May 2005, 03:41
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s and r are positive integers, is either r or s a prime?
1) r/s = 3/2
2) The greatest common divisor of r and s is 1



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Re: s and r are positive integers, is either r or s a prime? 1) [#permalink] New post   31 May 2005, 04:07
we can rewrite it to r = 1.5 s

when s = 2 r = 3 both prime

when s = 10 r = 15 boh not prime so I not SUFF

II is suff

Answer B
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Re: s and r are positive integers, is either r or s a prime? 1) [#permalink] New post   31 May 2005, 04:49
rxs0005 wrote:
we can rewrite it to r = 1.5 s

when s = 2 r = 3 both prime

when s = 10 r = 15 boh not prime so I not SUFF

II is suff

Answer B


Take r=21 s=25...their GCD is 1 but they are not prime....

I would go for E
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Re: s and r are positive integers, is either r or s a prime? 1) [#permalink] New post   31 May 2005, 10:15
sparky wrote:
s and r are positive integers, is either r or s a prime?
1) r/s = 3/2
2) The greatest common divisor of r and s is 1


I vote for C

1) Insufficient - could be (6,4) both not prime but (3,2) both prime.
2) Insufficient - could be (3,2) both prime or (6,35) both not prime

Using (1) and (2) r,s = 3,2

Theory, using 2) we can safely assume that r/s = was not reduced from someother fraction eg. 6/4 in which case GCD would not have been 1.
So r/s = 3/2 without any term getting cancelled , only possible when r=3 and s = 2 both prime.

HMTG.
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Re: s and r are positive integers, is either r or s a prime? 1) [#permalink] New post   31 May 2005, 17:14
Good one.

I) Insufficient. 2r = 3s

r = 6, s = 4

II) Insufficient

r = 22 , s = 27 Common factor = 1

So its either C or E.

If we combine them together we have 2r=3s and greatest common factor =1

We know because r and s are integers that any answer will have to be divisible by both multiple of 2 or 3 or else the equation would not work.

i.e. 2 (r=15) = 3 (s =10)

there will always be a common factor greater then 1... except when r/s = 2/3

C
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Re: s and r are positive integers, is either r or s a prime? 1) [#permalink] New post   31 May 2005, 21:37
1) r/s = 3/2
insufficient (3,2; 6,4)

2) The greatest common divisor of r and s is 1
Insufficient (2,3; 6,35)

Combine:
2r=3s
meaning s is multiple of 2 and r is multiple of 3.
Let r=3k, s=2m
2r=6k=3s=6m
=>k=m
k=m would be a common divisor of r and s. If the greatest common divisor is 1, then k=m=1. It follows that r=3, s=2. Both are prime numbers.

Sufficient.

C
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Re: s and r are positive integers, is either r or s a prime? 1) [#permalink] New post   01 Jun 2005, 10:47
My answer (and therefore OA :) ) is C

1. the ratio doesn;t do anything to show they are primes
2. if GCD is 1 doesn't mean numbers are prime (14 and 15 for example)

together, however, they work out alright



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Re: s and r are positive integers, is either r or s a prime? 1) [#permalink]
01 Jun 2005, 10:47
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