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A is insufficient as if N = 1 then 2N, i.e 2*1 = 2 has just one prime divisor.
if N = 2, then 2N, 2*2 also has ust one prime divisor i.e 2
so inufficient.

B.....3N if N = 1, then one prime divisor i.e 3
else for neother value of N, it will have more than one divisor.
hence B is sufficient.

1) if 2N has 1 prime divisor, N=2 (1 prime divisor ) or N=1 (no prime divisors) so insuff.

2) as above so insuff.

(1) + (2) imply that N=1, so it has no prime divisors so it is sufficient

Deowl, sorryr for being a dumbo. I still dont get it.

2N has 1 prime divisor. Doesnt that mean N can only take the value of 1?
ie. N=1 , only one prime divisor (2),
N=2, two prime divisors (2,2)
N=3, two prime divisors (2,3)

So, only N=1 satisfies this equation.

Can you pls tell me where I have gone wrong in my understanding?

Deowl, sorryr for being a dumbo. I still dont get it.

2N has 1 prime divisor. Doesnt that mean N can only take the value of 1? ie. N=1 , only one prime divisor (2), N=2, two prime divisors (2,2) N=3, two prime divisors (2,3)

So, only N=1 satisfies this equation.

Can you pls tell me where I have gone wrong in my understanding?

When you are counting factors (divisors) of an integer, you should only count different ones.

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