Sri,

As you evaluate (1), both your plug-ins give k more prime factors than j, but when you plug in, do your best to get conflicting answers. In other words, come up with a plug-in that gives j more prime factors (ex: j=2*3*5).

Likewise when you evaluate (2), you only used example that give k few prime factors. As a result you get the same answer to the original question. If you choose to plug-in, your instinct ought to be "how can I can different answers and prove insufficiency?" You could have given k more prime factors by plugging in k=2*3*5*7.


I would solve this using logic rather than plug in, by using the the fact that as you raise a number to higher powers, you don't introduce any new prime factors; you just multiply the existing primes by themselves..

1) k=10^j. k = 10*10*10... From this we know that the only prime factors of k are 2 and 5 (no new number will appear, only 10s). There is no restriction on the value of j, so j could have fewer or more prime factors than k. INSUFFICIENT.

2) j=30^k means j = 30*30*30... From this we know that the only prime factors of j are 2, 3, and 5. There is no restriction on the value of k, so k could have more or fewer prime factors than j.

TOGETHER: We know how many prime factors each variable has, so SUFFICIENT.

-Patrick

gmattesttaker2 wrote:Hello,

Can you please help with this problem:

If k & j are positive integers, and k is not equal to j, does k have more different prime factors
than j?

(1) k = (10)^j
(2) j = (30)^k

Statement 1 isn't sufficient, as we can see from a few numbers: suppose j = 1, in which case k has more prime factors; then suppose j = 30, in which case j has more prime factors. Statement 2 is much the same.

Taking the two together, k = (2*5) to the j power. We don't know how many different FACTORS k has, but we DO know how many different prime factors it has: two, just 2 and 5! Likewise with j, we have no idea how many factors it is, but we know about its prime factors: there are three of them, 2, 3, and 5. So with the two together, we can say the set {2, 3, 5} has more members than the set {2, 5}, so j has more unique prime factors than k does. Sufficient!