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

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

DS Question, I don't buy the answer.

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?


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.

I think what you're missing is this:

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.

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

p^3 − q^3 = (p−q)(p^2 + pq + q^2)

A should be OA.

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

p^3 -q^3 = (p-q)(p^2+pq+q^2)

Case 1: If p-q=0

The value of p^3 -q^3=0
=> Stmt 1 is suff.
(A/D can be option)
Case 2: if p+q=0

The value is in terms of p or q which is we still have one variable which is not definite value.
=>stmt is not suff.
(D can't be option)

OA is A.

Hope my approach is correct anyway.
(1) p-q=0 => p = q. So, p^3 - q^3 = 0 (since p=q)
Sufficient.

(2) p+q = 0; => p = -q. So, p^3 - q^3 results:
2p^3 or -2q^3. We don't know the values of p and q;
Insufficient

Ans : A from S1=we can say P=Q so for all Ans is 0

Option A is answer.
Formulae for p^3 − q^3 = (p-q)(p^2+pq+q^2)

Option 1 is enough.

stmt 1: \(p-q=0 so, p=q i.e. p^3=q^3\)
So, \(P^3-q^3=0\)

smt 2: \(p+q=0\). Can't say anything from here

So answer is A
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\(X^3+Y^3=(X+Y)*(X^2-XY+Y^2)\)
\(X^3-Y^3=(X-Y)*(X^2+XY+Y^2)\)

(1)
p = q

p^3 - q^3 = 0

Sufficient


(2)
p+q = 0

Not sufficient

p = q = 0 => p^3 - q^3 = 0

p = 1, q = -1 => 1 - (-1) = 2

Answer - A
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BELOW ALGEBRAIC FORMULA'S CAN BE USED
1. a^3 − b^3 = (a−b)(a^2 + ab + b^2)
2. a^3 + b^3 = (a+b)(a^2 − ab + b^2)
3.a^3 − b^3 = (a−b)^3 + 3ab(a − b)

STATEMENT 1 IS SUFFICIENT.

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.
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I got it wrong but the OA is A

as statement 1 implies that |p| = |q| and they are of same sign or p and q both are zero, then only statement 1 holds good.

what level is this question?
looks more like a 500-600 type question....
straightforward (A)

What is the value of p^3 - q^?

\(x^3-y^3=(x-y)(x^2+xy+y^2)\) (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.

Answer: A.
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p³ – q³ = (p – q)(p² + pq + q²)
you know thpt
(p – q)³ = p³ + 3pq(p – q) – q³
then p³ – q³ = (p – q)³ + 3pq(p – q)
= (p – q)[(p – q)² + 3pq]
= (p – q)(p² – 2pq + q² + 3pq)
= (p – q)(p² + pq + q² )

Choice 1 is sufficient to conclude that p³ – q³ =0 as p-q =0

p^3-q^3 = (p-q)(p^2+q^2+pq)

A is enough

B won't tell the value of the whole expression