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OE: From statement (1) it is clear that \(p=q\) , so the initial difference is 0. Absolutely enough. Statement (2) doesn't give any additional information. So, the answer is A.

In #2, q = -p, or the opposite of p. So p + q = 0, then if p = 2, then q = -2. So that 2 + -2 = 0. Works. Now apply this to \(p^3 - q^3\)

First try p = 2 and q = -2: \(2^3 - (-2)^3 = 8 - - 8 = 16\)

Now try p = -2 and q = 2: \((-2)^3 - 2^3 = -8 - 8 = -16\)

In both situations, p + q = 0, but when used in the equation given in the stem, we get different values so the statement cannot be sufficient, and therefore, A must be the answer since B is insufficient.

x-ALI-x wrote:

DS Question, I don't buy the answer.

Question: What is the value of \(p^3 - q^3\) ?

1. \(p - q = 0\) 2. \(p + q = 0\)

I answered D. Reasoning: \(p^3 - q^3\) = (p - q) (p + q) (p - q)

OA is A. OE: From statement (1) it is clear that \(p=q\) , so the initial difference is 0. Absolutely enough. Statement (2) doesn't give any additional information. So, the answer is A

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

I answered D. Reasoning: \(p^3 - q^3\) = (p - q) (p + q) (p - q) statement 1: (p-q) = 0, then \(p^3 - q^3 = 0\) statement 2: (p+q) = 0, then \(p^3 - q^3 = 0\)

Am I missing something?

OA is A. OE: From statement (1) it is clear that \(p=q\) , so the initial difference is 0. Absolutely enough. Statement (2) doesn't give any additional information. So, the answer is A

In fact, you got incorrect formula for p^3 - q^3. it is:

OA is A. OE: From statement (1) it is clear that \(p=q\) , so the initial difference is 0. Absolutely enough. Statement (2) doesn't give any additional information. So, the answer is A.

Its A. p^3 - q^3 = (p-q)(p^2+q^2+pq) hence 1 is enough.

\((p-q)^3=p^3-q^3-3pq(p-q)\) \(p^3-q^3=(p-q)^3+3pq(p-q)\) case 1.\(p-q =0\) \(p^3-q^3=(0)^3+3pq(0)\) \(p^3-q^3=(0)\) case 2. \(p+q=0\) implies \(p=-q\) \(p^3-q^3=(-q-q)^3+3(-q)q(-q-q)\) \(p^3-q^3=-8q^3+6q^3\) \(p^3-q^3=-2q^3\) (which is dependent on value of q : insufficient)

Seems A is right
_________________

Sun Tzu-Victorious warriors win first and then go to war, while defeated warriors go to war first and then seek to win.

OA is A. OE: From statement (1) it is clear that \(p=q\) , so the initial difference is 0. Absolutely enough. Statement (2) doesn't give any additional information. So, the answer is A.

Yes you are missing something and that is the correct factorization of \(p^3 - q^3\) which is \((p-q)*(p^2+p*q+q^2)\).

And as the p+q is not a factor we won't be able to get an answer based on p+q=0 so st2 is insufficient.
_________________

\(x^3-y^3=(x-y)(x^2+xy+y^2)\) (and \(x^3+y^3=(x+y)(x^2-xy+y^2)\)), but if you don't know this formula you can do just by substitution, which might be an easier way:

(1) \(p-q=0\) --> \(p=q\) --> \(p^3-q^3=p^3-p^3=0\). Sufficient. (2) \(p+q=0\) --> \(q=-p\) --> \(p^3-q^3=p^3-(-p^3)=2p^3\), so the value we are looking for depends on the value of \(p\). Not sufficient.