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Practice Question of the Week #2: Win a Premium Subscription to Magoosh GRE!

Integer properties:

If k is an non-negative integer and 15^k is a divisor of 759,325 then 3^k-k^3=

A. 0
B. 1
C. 37
D. 118
E. 513

The answer will be posted tomorrow afternoon, and we’ll be choosing another winner to receive a free premium subscription to the Magoosh GRE product to help you study!

Submit a correct answer and explanation by commenting on this post or head over to our facebook with your response before 1PM Pacific Daylight Time tomorrow and we will select any one of the readers with the correct answer to win.

This is a pretty touch challenge problem, good luck!


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Update: Here’s the answer/explanation post!

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4 Responses to Practice Question of the Week #2: Win a Premium Subscription to Magoosh GRE!

  1. Ashok Kumar June 8, 2011 at 10:57 am #


    (B) 1


    For divisibility by 15, the number should be divisible by both 3 and 5.
    Checking divisibility by 3, we find that it is not divisible. Because 7 + 5 + 9 + 3 + 2 + 5 = 31 which is not divisible by 3. Hence 15 or any multiple of 15 cannot divide that number exactly. Hence the only possible solution is k = 0.

    If k = 0, then 3^0 – 0^3 => 1 – 0 => 1

    • Margarette Jung
      margarette June 8, 2011 at 2:55 pm #

      Ashok, I just sent you an e-mail that explains how to claim your prize. Congrats!

  2. Nirav June 7, 2011 at 11:15 am #

    The answer is B.
    As 15 is not a divisor of 759325, neither are any powers of 15.
    Therefore k is 0. 15^1 is 1, which is a divisor of 759325.
    3^0 – 0^3 = 1

  3. Karthik Chockkalingam June 7, 2011 at 11:05 am #

    Ans is 1.
    15 Power 1 is 15 and it is not a divisor of the given number.And hence the higher power of 15 will not be a divisor of the given number. For instance, If we take 15 power 5, the value is 759,375.
    Therefore the only possibility is 15 Power 0 is 1 and we know that 1 is a divisor for all the numbers. The value of K is 0.
    Substituting this, we have (3^0)-(0^3) ans it is simplified as 1-0=1. Hence the solution is arrived.

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