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

This topic has 4 expert replies and 0 member replies

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

Post Fri Nov 10, 2017 6:08 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the value of p^3 - q^3?

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

    The OA is A .

    How can I use p-q=0 to get the value of p^3-q^3? And why p+q=0 is not sufficient?

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    Post Fri Nov 10, 2017 6:39 am
    Vincen wrote:
    What is the value of p^3 - q^3?

    (1) p - q = 0
    (2) p + q = 0
    Statement 1:
    Thus, p=q.
    Substituting p=q into p³ - q³, we get:
    p³ - q³ = p³ - p³ = 0.
    SUFFICIENT.

    Statement 2:
    If p=0 and q=0, then p³ - q³ = 0³ - 0³ = 0.
    If p=1 and q=-1, then p³ - q³ = 1³ - (-1)³ = 1 +1 = 2.
    Since p³ - q³ can be different values, INSUFFICIENT.

    The correct answer is A.

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    Post Fri Nov 10, 2017 10:52 am
    Hi Vincent,

    We're asked for the value of P^3 - Q^3. This question can be solved with a mix of TESTing VALUES and Number Property rules.

    1) P - Q = 0

    With Fact 1, we know that P and Q have to be the SAME number (since subtracting Q from P equals 0). Thus, regardless of what value we use for P and Q, we'll end up with the equal values for P^3 and Q^3. Thus, the answer to the question is ALWAYS 0.
    Fact 1 is SUFFICIENT

    2) P + Q = 0

    With Fact 2, we can easily TEST VALUES and track the results:
    IF....
    P=0, Q=0, then 0^3 - 0^3 = 0 and the answer to the question is 0
    P=1, Q = -1, then 1^3 - (-1)^3 = 2 and the answer to the question is 2
    Fact 2 is INSUFFICIENT

    Final Answer: A

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    Post Fri Nov 10, 2017 1:07 pm
    Any time we have one cube minus another, we can factor like so:

    p³ - q³ =>

    (p - q) * (p² + pq + q²)

    So if we're told (p - q) = 0, p³ - q³ is 0 * (p² + pq + q²), or 0.

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    Post Fri Nov 10, 2017 1:08 pm
    Alternatively, if p - q = 0, we can say that p = q, and that p³ - q³ = p³ - p³ = 0.

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