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prime numbers

by vipulgoyal » Mon Apr 22, 2013 1:44 am
. Integer N is greater than 0. is N a prime number?
1). All the prime factors of N are greater than root N
2). All the prime factors of N are greater than N/2

please suggest both cases if N is greater then 0 or if may or may not be greater then 0
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by Jim@StratusPrep » Mon Apr 22, 2013 5:08 am
Both of these statements are sufficient. There are no cases when N is composite and this is true.

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by Lifetron » Mon Apr 22, 2013 5:25 am
Jim@StratusPrep wrote:Both of these statements are sufficient. There are no cases when N is composite and this is true
Can you explain this ?

Thank you !
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by srcc25anu » Mon Apr 22, 2013 11:08 am
Given N is integer > 0.

St1: All prime factors of N greater than root of N

if n = 3, prime factor of 3 = 3; root3 = 1.7 PRIME FACTOR is GREATER THAN ROOT(N).
if n = 5, prime factor of 5 = 5; root5 = 2.1 PRIME FACTOR is GREATER THAN ROOT(N).
For PRIME FACTOR TO BE GREATER THAN ROOT(N), N must be prime.
hence SUFFICIENT

St2: All prime factors of N greater than n/2
if n = 3, prime factor of 3 = 3 and n/2 = 1.5 PF > N/2
if n = 5, prime factor of 5 = 5 and n/2 = 2.5 PF > N/2

if I check for n = (Npn-Prime)6, n/2 = 3 and prime factors of 6 = 2,3. One prime factor in this case (2) is LESS than n/2 and one prime factor (3) is EQUAL TO n/2. None of the prime factors is greater than n/2 PF <= N/2
Hence B also looks SUFFICIENT

IMO D
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by burningman » Tue Apr 23, 2013 7:56 pm
What about 1 ? Prime factors of 3 are 3 and 1.
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by Brent@GMATPrepNow » Tue Apr 23, 2013 8:02 pm
burningman wrote:What about 1 ? Prime factors of 3 are 3 and 1.
1 is not prime.

Definition: A prime number is a positive integer that has exactly two different positive divisors

1 has only one divisor, so it is not prime.

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by Lifetron » Tue Apr 23, 2013 8:07 pm
burningman wrote:What about 1 ? Prime factors of 3 are 3 and 1
1 is not prime
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