prime numbers are factors

[sanju09]

How many different prime numbers are factors of the positive integer n?

(1) Four different prime numbers are factors of 2 n.

(2) Four different prime numbers are factors of n ^ 2.

[bluementor]

Statement 1: 2n has 4 different prime factors.

n could have 2 as a prime factor -> n has 4 different prime factors.
n may not have 2 as a prime factor -> n has 3 different prime factors.

Insufficient.

Statement 2: n^2 has 4 different prime factors.

Sufficient. If n^2 has 4 different prime factors, then n will have the same exact prime factors.

Choose B.

-BM-

[vittalgmat]

Statement 1: 2n has 4 different prime factors.

n could have 2 as a prime factor -> n has 4 different prime factors.
n may not have 2 as a prime factor -> n has 3 different prime factors.



Insufficient.

Statement 2: n^2 has 4 different prime factors.

Sufficient. If n^2 has 4 different prime factors, then n will have the same exact prime factors.

Choose B.

-BM-

Could not understand how u can have a number 2n and not have 2 as its prime factor. Can u pls give me an example.
thanks

[cramya]

Vittal,

n = 3*5*7

2n has 4 different prime factors.

n = 2*3*5*7

Still 2n has 4 different prime factors.

Hence stmt I is INSUFF

Stmt II is SUFF since n^2 has the same prime factors as n.

Hope this helps!

Regards,
CR

[vittalgmat]

Statement 1: 2n has 4 different prime factors.

n could have 2 as a prime factor -> n has 4 different prime factors.
n may not have 2 as a prime factor -> n has 3 different prime factors.



Insufficient.

Statement 2: n^2 has 4 different prime factors.

Sufficient. If n^2 has 4 different prime factors, then n will have the same exact prime factors.

Choose B.

-BM-

Could not understand how u can have a number 2n and not have 2 as its prime factor. Can u pls give me an example.
thanks

@bluementor

OOps my mistake!!! dint think thru ur explanation. Somehow my mind tricked me into reading "2n may not have 2 as a prime factor!!! "

2n has and should have 2 as its prime factor BUT
n need not have have 2 as its prime factor...

My solution is similar to u and Cramya.