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

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Manager
Status: 2 months to go
Joined: 11 Oct 2015
Posts: 128
GMAT 1: 730 Q49 V40
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For how many positive integers n is it true that...  [#permalink]

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06 Jul 2016, 06:41
5
00:00

Difficulty:

55% (hard)

Question Stats:

56% (00:47) correct 44% (00:57) wrong based on 84 sessions

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

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06 Jul 2016, 08:55
1
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

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

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06 Jul 2016, 09:47
1
1
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

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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28 Oct 2017, 21:10
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