Taking out common

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Taking out common

by [email protected] » Sun Jul 27, 2014 7:01 am
What is the value of p^3 −q^3 ?

(1) p−q=0

(2) p+q=0


I was trying to solve this with this way (p-q)(p^2-q^2) i.e. (p-q)(p+q)(p-q), where Am I going wrong?

Thanks

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by Brent@GMATPrepNow » Sun Jul 27, 2014 7:10 am
[email protected] wrote:What is the value of p³ − q³?

(1) p − q = 0
(2) p + q = 0
Target question: What is the value of p³ − q³?

This question requires you to know how to factor a DIFFERENCE OF CUBES (which is not required on the GMAT).
The factoring is as follows: a³ - b³ = (a - b)(a² + ab + b²)
So, we can REPHRASE the target question as follows:

REPHRASED target question: What is the value of (p - q)(p² + pq + q²)?

Statement 1: p − q = 0
If p - q = 0, then (p - q)(p² + pq + q²) = (0)(p² + pq + q²) = 0
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: p + q = 0
There are several values of p and q that satisfy this condition. Here are two:
Case a: p = 0 and q = 0, in which case p³ − q³ = 0
Case b: p = 1 and q = -1, in which case p³ − q³ = 2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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by GMATGuruNY » Sun Jul 27, 2014 7:56 am
[email protected] wrote:What is the value of p^3 −q^3 ?

(1) p−q=0

(2) p+q=0
Statement 1: p-q=0
Thus:
p=q, implying that p³ = q³ and that p³ - q³ = 0.
SUFFICIENT.

Statement 2: p+q = 0
If p=1 and q=-1, then p³ - q³ = 1 - (-1) = 2.
If p=-1 and q=1, then p³ - q³ = -1 - 1 = -2.
Since p³ - q³ can be different values, INSUFFICIENT.

The correct answer is A.
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by GMATinsight » Sun Jul 27, 2014 9:39 am
[email protected] wrote:
What is the value of p³ - q³?

(1) p - q = 0
(2) p + q = 0
USING ANOTHER PROPERTY

(p - q)³ = p³ - q³ - 2pq (p - q)

i.e. Question : p³ - q³ = (p - q)³ + 2pq (p - q) = ?

Statement 1) p - q = 0

i.e. p³ - q³ = 0 + 0 = 0
SUFFICIENT

Statement 1) p + q = 0
Neither Gives us P-q nor does it give us pq, therefore
INSUFFICIENT

Answer: Option A
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by BestGMATEliza » Sun Aug 03, 2014 8:43 pm
For a lot of problems like these factoring is a good first step, however for this one I think it is unnecessary, since the factored inequality seems to complicate things.

(1) from this we know that p=q, so p^3-q^3 must equal 0. SUFFICIENT

(2) from this we know that p=-q. However we don't know if p is the negative or q is the negative or if they are both 0, so we can't know what p^3-q^3 is.
Say they were both 0, then p^3-q^3 would equal 0. However, p could be 1 and q could be -1 and then p^3-q^3 would equal 2.

So, the answer is A
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by [email protected] » Mon Aug 04, 2014 12:21 pm
Hi shibsriz,

As you can see, there are a variety of ways to approach this question. In many cases, the "math" approach requires more work than a strategic one.

You can use Number Properties to solve this problem:

We're asked for the value of P^3 - Q^3?

Fact 1: P - Q = 0

This means that P = Q, so they're....
Both the SAME POSITIVE NUMBER, in which case the answer to the question is 0
or
Both the SAME NEGATIVE NUMBER, in which case the answer to the question is 0
or
Both 0, in which case the answer to the question is 0
Fact 1 is SUFFICIENT

Fact 2: P + Q = 0

This means that P = -Q
IF they're.....
Both 0, then the answer to the question is 0
One POSITIVE and One NEGATIVE, then the answer to the question is either a NEGATIVE NUMBER or a POSITIVE NUMBER (depending on which variable is positive and which is negative).
Fact 2 is INSUFFICIENT

Final Answer: A

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