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If u > 0 and v > 0, which is greater

This topic has 2 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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If u > 0 and v > 0, which is greater

Post Mon Jul 24, 2017 9:28 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If u > 0 and v > 0, which is greater, u^v or v^u?
    (1) u = 1
    (2) v > 2

    Official Guide question
    Answer: C

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    Post Mon Jul 24, 2017 5:07 pm
    Using Statement 1, if u = 1, then

    u^v = 1^v = 1

    and

    v^u = v^1 = v

    So the question "which is greater, u^v or v^u?" becomes "which is greater, 1 or v?" We don't know if v is greater than 1 (we only know that v > 0) so Statement 1 is not sufficient. But when we use both statements, we know v > 2, so v is certainly greater than 1, and the answer is C.

    Statement 2 is not sufficient alone. We just saw above that v^u can be larger, but using only statement 2, it might be that u = 3 and v = 3, say, and then neither of u^v or v^u is larger than the other, so we can get two different answers to the question only using Statement 2. Other sets of values will prove that as well - I think the OG solution uses u = 3 and v = 4.

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    Post Mon Jul 24, 2017 5:27 pm
    Hi jjjinapinch,

    This question can be solved by TESTing VALUES.

    We're told that both U and V are POSITIVE (and while that doesn't necessarily mean that they have to be positive integers, we can use integers to get to the correct answer). We're asked whether U^V or V^U is greater. This is the equivalent of a YES/NO question.

    1) U = 1

    IF.....
    V = 1
    then 1^1 and 1^1 are the SAME value, so NEITHER is greater.

    IF....
    V = 2
    then 1^2 = 1 and 2^1 = 2, so V^U is greater.
    Fact 1 is INSUFFICIENT

    2) V > 2

    IF....
    V = 3, U = 1
    then 1^3 = 1 and 3^1 = 3, so V^U is greater.

    IF....
    V = 3, U = 3
    then 3^3 and 3^3 are the SAME value, so NEITHER is greater.
    Fact 1 is INSUFFICIENT

    Combined, we know....
    U = 1 and V > 2
    U^V will always be 1^(something > 2) = 1 and V^U = (something greater than 2)^1 = that same value greater than 2. Thus, V^U will ALWAYS be greater.
    Combined, SUFFICIENT

    Final Answer:
    C

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