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Prime and Composite

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by sparkles3144 » Mon May 27, 2013 10:12 pm
I found this in GMAT Prep Now Data Sufficiency.
I just want to understand it.

If K is an integer greater than 1, and S is the sum of all positive divisors of K, is S > K+1?

So in GMAT Prep Now Video, they paraphrased it to "Is K not prime?"

I just wanted to know how one can tell using give information that K is not prime.

Thanks!
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by mkdureja » Tue May 28, 2013 12:02 am
sparkles3144 wrote:I found this in GMAT Prep Now Data Sufficiency.
I just want to understand it.

If K is an integer greater than 1, and S is the sum of all positive divisors of K, is S > K+1?

So in GMAT Prep Now Video, they paraphrased it to "Is K not prime?"

I just wanted to know how one can tell using give information that K is not prime.

Thanks!
Prime numbers are defined as the numbers whose only positive divisors are 1 and the number itself.
Sum of all positive divisors of a prime number, lets say k is therefore: 1+k;
s=1+k for all primes
For non-primes, you must have at least 1 more positive divisor, so in that case:
s>1+k for all non-primes
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by mkdureja » Tue May 28, 2013 12:03 am
sparkles3144 wrote:I found this in GMAT Prep Now Data Sufficiency.
I just want to understand it.

If K is an integer greater than 1, and S is the sum of all positive divisors of K, is S > K+1?

So in GMAT Prep Now Video, they paraphrased it to "Is K not prime?"

I just wanted to know how one can tell using give information that K is not prime.

Thanks!
Prime numbers are defined as the numbers whose only positive divisors are 1 and the number itself.
Sum of all positive divisors of a prime number, lets say k is therefore: 1+k;
s=1+k for all primes
For non-primes, you must have at least 1 more positive divisor, so in that case:
s>1+k for all non-primes
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