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prime factor DS

by fangtray » Wed Apr 04, 2012 5:53 am
If r and S are positive integers, is r/s an integer?

1) every factor of S is also a factor of r
2) every prime factor of S is also a prime factor of r.

1. sufficient.
2. Should be sufficient right?

for example, if S = 2*2*5*7*11*11*13, then doesn't statement 2 mean that r has all those prime factors and maybe more?
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by Pharo » Wed Apr 04, 2012 6:04 am
1. Sufficient; as you say.
2. Not sufficient; since it is possible to satisfy this case and have an s greater than r. An example would be r = 5 and s = 25.

Answer should be A :)
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by Bill@VeritasPrep » Wed Apr 04, 2012 7:06 am
Pharo wrote:1. Sufficient; as you say.
2. Not sufficient; since it is possible to satisfy this case and have an s greater than r. An example would be r = 5 and s = 25.

Answer should be A :)
I love using questions similar to this with tutoring students because the vast majority of GMAT takers would assume that Statement 2 means r must be greater than s. It's a great illustration of how careful we have to be with Data Sufficiency.
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by fangtray » Thu Apr 05, 2012 5:58 am
Bill@VeritasPrep wrote:
Pharo wrote:1. Sufficient; as you say.
2. Not sufficient; since it is possible to satisfy this case and have an s greater than r. An example would be r = 5 and s = 25.

Answer should be A :)
I love using questions similar to this with tutoring students because the vast majority of GMAT takers would assume that Statement 2 means r must be greater than s. It's a great illustration of how careful we have to be with Data Sufficiency.
I thought of this scenario while i was taking the practice test. i figured statement 2 meant that S = 5*5 and r would need to have at least those 2 prime numbers as well. because it says EVERY prime factor...it doesn't say every distinct prime factor. i imagine every prime factor includes, 5 and any other 5 which is also a prime factor, just like the previous 5.
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by Pharo » Thu Apr 05, 2012 7:02 am
It says "every" but it does not say "how many". I was given this great advice: "do not assume anything in gmat questions" :)
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by dchhikara863 » Thu Apr 05, 2012 7:43 pm
That assumption of considering 5 twice as an example of considering all prime factors would be incorrect.

If I asked you the prime factors of 24, they'd be 2 and 3. not 2,2,3 etc.

Same way, 25 has only one prime factor 5. Not 5 and 5.

Therefore, in this case if r = 18 and S = 24, the prime factors 2 and 3 are common however, r/s is not an integer

In addition, I was also told that GMAT rarely ever over-tricks you. So its pointless to over analyze :)
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by Anurag@Gurome » Fri Apr 06, 2012 6:18 am
fangtray wrote:If r and S are positive integers, is r/s an integer?

1) every factor of S is also a factor of r
2) every prime factor of S is also a prime factor of r.

1. sufficient.
2. Should be sufficient right?

for example, if S = 2*2*5*7*11*11*13, then doesn't statement 2 mean that r has all those prime factors and maybe more?
(1) Every factor of S is also a factor of R implies when S will be reduced in R/S, we get an integer; SUFFICIENT.

(2) Every prime factor of S is also a prime factor of R. The powers of primes factors of S could be higher than powers of prime factors of R; NOT sufficient.

The correct answer is A.
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