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# M01 #12

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M01 #12 [#permalink]  02 Jan 2009, 20:40
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What is the value of $$p^3 - q^3$$ ?

1. $$p - q = 0$$
2. $$p + q = 0$$

$$p^3 - q^3$$ = (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.
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Re: m01#12 [#permalink]  02 Jan 2009, 21:51
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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.

x-ALI-x wrote:

Question:
What is the value of $$p^3 - q^3$$ ?

1. $$p - q = 0$$
2. $$p + q = 0$$

$$p^3 - q^3$$ = (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

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Re: m01#12 [#permalink]  03 Jan 2009, 09:57
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x-ALI-x wrote:

Question: What is the value of $$p^3 - q^3$$ ?

1. $$p - q = 0$$
2. $$p + q = 0$$

$$p^3 - q^3$$ = (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:

p^3 − q^3 = (p−q)(p^2 + pq + q^2)

A should be OA.
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Re: M01 #12 [#permalink]  10 May 2010, 07:30
xALIx wrote:
What is the value of $$p^3 - q^3$$ ?

1. $$p - q = 0$$
2. $$p + q = 0$$

[Reveal] Spoiler: OA
A

$$p^3 - q^3$$ = (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.

Its A.
p^3 - q^3 = (p-q)(p^2+q^2+pq) hence 1 is enough.
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Re: M01 #12 [#permalink]  10 May 2010, 08:53
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$$(p-q)^3=p^3-q^3-3pq(p-q)$$
$$p^3-q^3=(p-q)^3+3pq(p-q)$$
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
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Re: M01 #12 [#permalink]  10 May 2010, 10:26
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.
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Re: M01 #12 [#permalink]  10 May 2010, 13:14
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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
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Re: M01 #12 [#permalink]  10 May 2010, 19:17
Ans : A from S1=we can say P=Q so for all Ans is 0
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Re: M01 #12 [#permalink]  11 May 2010, 03:58
Formulae for p^3 − q^3 = (p-q)(p^2+pq+q^2)

Option 1 is enough.
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Re: M01 #12 [#permalink]  20 May 2010, 05:03
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

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Re: M01 #12 [#permalink]  08 Nov 2010, 16:13
$$X^3+Y^3=(X+Y)*(X^2-XY+Y^2)$$
$$X^3-Y^3=(X-Y)*(X^2+XY+Y^2)$$
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Re: M01 #12 [#permalink]  12 May 2011, 04:08
(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

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Re: M01 #12 [#permalink]  12 May 2011, 18:18
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.
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Re: M01 #12 [#permalink]  13 May 2011, 03:27
xALIx wrote:
What is the value of $$p^3 - q^3$$ ?

1. $$p - q = 0$$
2. $$p + q = 0$$

[Reveal] Spoiler: OA
A

$$p^3 - q^3$$ = (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.

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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Re: M01 #12 [#permalink]  14 Jan 2012, 21:03
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.
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Re: M01 #12 [#permalink]  16 May 2012, 04:28
what level is this question?
looks more like a 500-600 type question....
straightforward (A)
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Re: M01 #12 [#permalink]  16 May 2012, 07:31
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Expert's post
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.

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Re: M01 #12 [#permalink]  20 May 2013, 06:50
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
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Re: M01 #12 [#permalink]  23 May 2013, 19:11
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p^3-q^3 = (p-q)(p^2+q^2+pq)

A is enough

B won't tell the value of the whole expression
Re: M01 #12   [#permalink] 23 May 2013, 19:11
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