Product of two integers

[metallicafan]

Can the positive integer k be expressed as the product of two integers, each of which is greater than 1?
(1) k^2 has one more positive factor than k.
(2) 11 < k < 19

I don't understand well this explanation of the OE. Please, your help:
The only types of numbers k such that k2 has exactly one more positive factor than k are primes. Prime numbers have two factors and their squares have three. If k had more than two factors, the number of factors would increase by more than 1 when squared. Thus, k must be prime, answering the question.

[Anurag@Gurome]

Can the positive integer k be expressed as the product of two integers, each of which is greater than 1?
(1) k^2 has one more positive factor than k.
(2) 11 < k < 19

I don't understand well this explanation of the OE. Please, your help:
The only types of numbers k such that k2 has exactly one more positive factor than k are primes. Prime numbers have two factors and their squares have three. If k had more than two factors, the number of factors would increase by more than 1 when squared. Thus, k must be prime, answering the question.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Here we have to find if k is a prime number.

(1) k² has one more positive factor than k.
If k is a prime then it has 2 factors, 1 and k implies k² has 3 factors: 1, k, and k².
If k = 1 (not a prime number), then k² will have the same number of factor as k.
Hence k has to be a prime; SUFFICIENT.

(2) 11 < k < 19.
If k = 12, it is not a prime.
If k = 13, it is prime; NOT Sufficient.

The correct answer is A.

[anuprajan5]

Anurag,

Isn't the question asking us to prove that k is non-prime?

Can the positive integer k be expressed as the product of two integers, each of which is greater than 1

I get the reasoning in statement 1 and 2. But the rephrase of the question seems to be wrong.

[Brent@GMATPrepNow]

Anurag,

Isn't the question asking us to prove that k is non-prime?

Can the positive integer k be expressed as the product of two integers, each of which is greater than 1

I get the reasoning in statement 1 and 2. But the rephrase of the question seems to be wrong.

Both rephrased target questions ("Is k prime?" and "Is k non-prime?") are essentially the same in that a statement that is sufficient to answer one rephrased target question will be sufficient to answer the other rephrased target question.

For example, if we are able to conclude, with certainty, that k is prime, then we can also conclude, with certainty, that k is not non-prime.

Cheers,
Brent