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For how many positive integers n is it true that...

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For how many positive integers n is it true that... [#permalink]

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New post 06 Jul 2016, 05:41
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For how many positive integers n is it true that the sum of 13/n, 18/n, and 29/n is an integer?
(A) 6
(B) 60
(C) Greatest common factor of 13, 18, and 29
(D) Least common multiple of 13, 18, and 29
(E) 12

Source: Nova's GMAT Math Prep Course
[Reveal] Spoiler: OA

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Re: For how many positive integers n is it true that... [#permalink]

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New post 06 Jul 2016, 07:55
13/n + 18/n + 29/n = 60/n

60/n will be an integer when n is a factor of 60

60 = 2^2 * 3 * 5
Number of factors = 3 * 2 * 2 = 12

Answer: E

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Re: For how many positive integers n is it true that... [#permalink]

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New post 06 Jul 2016, 08:47
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Vyshak wrote:
13/n + 18/n + 29/n = 60/n

60/n will be an integer when n is a factor of 60

60 = 2^2 * 3 * 5
Number of factors = 3 * 2 * 2 = 12

Answer: E


I write this just for the benefit of others (Because I had to search how this is done) :)

This is how the total number of factors for a given number is found

    1. Prime factorise the Number. Meaning, Write the number as the product of prime numbers (in our case \(60 = 2^2 * 3 * 5)\)
    2. Write down the exponents of all the prime factors (in our case - \(2,1,1\))
    3. Add one to each of these exponents (In our case - \(2+1=3, 1+1=2, 1+1=2\))
    4. Multiply all the numbers got above to get our answer(In our case - \(3*2*2 = 12\))

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Re: For how many positive integers n is it true that... [#permalink]

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New post 28 Oct 2017, 20:10
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Re: For how many positive integers n is it true that...   [#permalink] 28 Oct 2017, 20:10
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