IMO A.
Stmt1: I can't think of a number n that has (n+1) factors. There can be only 2 factors for a prime number, 1 & itself. Since we can answer this question by saying NO, this statement is sufficient.
Stmt2: (n+1) is not a prime number can be true with n is either a prime or a composite number, i.e. when n=3, (n+1)=4, but when n=8, (n+1)=9. So, this statement is not sufficient.
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Source: Beat The GMAT — Data Sufficiency |
n is prime can be (1, 2, 3, 5, 7, 11, 13, ... etc)
1) number of factors of n is n+1
if they are asking about distinct prime factors then none of the above choices can fit the n+1 criteria --> suff
if they are asking about ALL factors then 1 can have 1 and itselft (so 1) hence 2 factors = n+1 --> insuff
2) n+1 is not prime
there are several n+1 is not prime options, ie 3, 5, 7, 11, 13 -->insuff
so answer (assuming they are asking for distinct factors) is A otherwise it's C
1) number of factors of n is n+1
if they are asking about distinct prime factors then none of the above choices can fit the n+1 criteria --> suff
if they are asking about ALL factors then 1 can have 1 and itselft (so 1) hence 2 factors = n+1 --> insuff
2) n+1 is not prime
there are several n+1 is not prime options, ie 3, 5, 7, 11, 13 -->insuff
so answer (assuming they are asking for distinct factors) is A otherwise it's C
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Ian Stewart
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There's a good reason you can't think of such a number - there isn't one. The only possible positive factors of a number n are in the set {1, 2, 3, ..., n}, so clearly n can't have more than n positive factors. So the question doesn't make sense; where is it from?Vemuri wrote:IMO A.
Stmt1: I can't think of a number n that has (n+1) factors.
Two things here - note that 1 is not a prime number; 2 is the smallest prime. Also, 1 only has one positive factor - itself.m&m wrote:n is prime can be (1, 2, 3, 5, 7, 11, 13, ... etc)
if they are asking about ALL factors then 1 can have 1 and itselft (so 1) hence 2 factors = n+1 --> insuff
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mike22629
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I believe that it is A for what Ian said.
In order for a number to be prime, it can only have two factors, n and 1.
If the number of factors of n is n+1, then n can NOT be prime. This is because the only number that satisfies N having 2 factors is 1, which is not prime.
2.) is obviously insufficient.
But, this is a bad question because the question is technically saying that "1" has two factors.
As usual, Ian is all-knowing.
In order for a number to be prime, it can only have two factors, n and 1.
If the number of factors of n is n+1, then n can NOT be prime. This is because the only number that satisfies N having 2 factors is 1, which is not prime.
2.) is obviously insufficient.
But, this is a bad question because the question is technically saying that "1" has two factors.
As usual, Ian is all-knowing.
