N has 12 factors => N can be of the form p^11 or p*q^5 or p^2 * q^3. So, this is not sufficient

N^3 has 70 factors

70 can be written as

70 * 1 => N^3 = p^69 possible => N = p^ 23

35 * 2 => N^3 = p^34 * q Not possible as this cannot be a perfect cube

5 * 14 => N^3 = p^4 * q^13 Not possible as this cannot be a perfect cube

7 * 10 => N^3 = p^6 * q ^ 9 Possible => N = P^2 * q^3

So, this alone is not sufficient.

Both combined together, we can say N has to be of the form p^2 * q^3 and therefore number of factors of N^2 can be found.

Good question, but to be honest I do not think CAT will ask a question even as tough as this.

Cheers,

Rajesh

2IIM

On Wed, Aug 17, 2011 at 4:38 AM, mohit gupta

<mohit_luvkush@...> wrote:

data sufficiency

If N is a natural number then number of factors of N^2 is ...

A. N has 12 factors.

B. N^3 has 70 factors.

pls ans with xplanation