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Integer Properties Multiple Choice: Practice Question of the Week #25

Here’s this week’s practice question: there’s only one correct answer. We’ll be posting the answer tomorrow, good luck!

How many odd, positive divisors does 540 have?

A. 6

B. 8

C. 12

D. 15

E. 24


Update: Here’s the answer/explanation post!

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4 Responses to Integer Properties Multiple Choice: Practice Question of the Week #25

  1. MN November 15, 2011 at 4:16 pm #

    540 breaks down to 2^2 x 3^3 x 5. Since we’ve got only a handful, we can quickly list these out & count them – there are 8. Answer choice is “B”.
    However, if the resultant number was 3^24 x 5^19 – we simply can not count it out.
    If we choose all possible numbers forming out of 3^3 x 5 we’ll get,
    4 x 2 = 8
    (there are 4 ways to choose from 3^3, we can choose either 3^0 or 3^1 or 3^2 or 3^3; and there are 2 ways to choose from 5; we can choose 5^0 or 5^1).
    For the hypothetical case, 3^24 x 5^19, we’ll get 25 x 20 = 500. [As indicated earlier, this simply can’t be counted by listing each of the 500 numbers in a GRE test].

  2. lucym November 15, 2011 at 7:56 am #

    i will go with 8
    5^1 x 3^3=2×4=8

  3. marzu November 15, 2011 at 1:47 am #


  4. Mohamed November 14, 2011 at 12:57 pm #

    I’ll go with 8

    odd divisors: 1, 3, 5, 9, 15, 27, 45, 135

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