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OK I got this question wrong (I answered B but the OA is D) but I am not far of from grasping this whole integer properties bit. Can someone please clarify:

Statement 2: p^3 has exactly 4 distinct factors

What exactly does this statement mean? What should I be thinking of here? The "4 distinct factors" is not clear to me.

I get that B is suff. But A? even if P weren't prime say (12)^3 = P^3 = 12 is not prime. On the other hand, (2)^3 says P is prime. So a prime cubed and non prime cubed both will have 4 distinct factors (say 2 cubed has 4,8,2,1). Can someone explain why is A sufficient?

For statement 1 p^3 has exactly 4 distinct factors: 1,p,p^2,p^3. Hence prime, therefore sufficient.

For statement 2 when you factorize the equation you get x=2,3. Both are prime, therefore sufficient.

For statement 2, you get x = -2, 3.

sarahfiqbal wrote:

OK I got this question wrong (I answered B but the OA is D) but I am not far of from grasping this whole integer properties bit. Can someone please clarify:

Statement 2: p^3 has exactly 4 distinct factors

What exactly does this statement mean? What should I be thinking of here? The "4 distinct factors" is not clear to me.

Please please and thank you.

All "distinct factors" means all the positive, integer factors of a number counted only once. Distinct factors of 125 are 1, 5, 25, and 125.

Madhavi1990 wrote:

I get that B is suff. But A? even if P weren't prime say (12)^3 = P^3 = 12 is not prime. On the other hand, (2)^3 says P is prime. So a prime cubed and non prime cubed both will have 4 distinct factors (say 2 cubed has 4,8,2,1). Can someone explain why is A sufficient?

Look below.

Last edited by BlueOwl on 05 Nov 2017, 12:12, edited 2 times in total.

(1) p^3 has exactly 4 distinct factors (2) p^2 – p – 6 = 0.

Hi All,

We're told that P is POSITIVE. We're asked if P is PRIME. This is a YES/NO question. To start, it's worth noting that we do NOT know whether P is an integer or not (and if you assume that P must be an integer, then you'll get this question wrong).

1) P^3 has exactly 4 distinct factors.

To start, let's focus on numbers that have just 4 distinct factors. There are two that you should be able to find relatively easily: 6 (factors are 1, 2, 3 and 6) 8 (factors are 1, 2, 4 and 8)

According to Fact 1, P^3 could be either of those 2 numbers.... IF.... P^3 = 6, then P is a NON-INTEGER and the answer to the question is NO P^3 = 8, then P = 2 and the answer to the question is YES. Fact 1 is INSUFFICIENT

2) P^2 - P - 6 = 0

We can factor this equation into it's pieces and solve... P^2 - P - 6 = 0 (P-3)(P+2) = 0 P = +3 or -2 The prompt tells us that P is POSITIVE, so there's only one solution here: +3... and the answer to the question is ALWAYS YES. Fact 2 is SUFFICIENT

The catch is p is positive, but need not be an integer

Statement 1 : \(p^3\) has 4 distinct factors if \(p\) is prime, then \(p^3\) has 4 distinct factors BUT if \(p = x^{1/3} * y ^ {1/3}\), where x and y are prime numbers, then \(p^3 = (x^{1/3} * y ^ {1/3})^3 = xy\) still has 4 distinct factors, in this case p is not prime.

Not Suff

Statement 2: from quad eqn we can p = -2 or 3, since p is positive, p = 3, prime -> Suff