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
Taking out common
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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
Cheers,
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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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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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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
(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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich