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# For how many positive integers n is n/30−n also a positive integer?

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Senior Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 280
For how many positive integers n is n/30−n also a positive integer?  [#permalink]

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18 Mar 2019, 08:22
1
00:00

Difficulty:

65% (hard)

Question Stats:

43% (02:15) correct 57% (02:20) wrong based on 23 sessions

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For how many positive integers n is$$\frac{n}{30−n}$$ also a positive integer?

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8
Intern
Joined: 15 Aug 2018
Posts: 2
Re: For how many positive integers n is n/30−n also a positive integer?  [#permalink]

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18 Mar 2019, 08:30

Posted from my mobile device
Senior Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 280
For how many positive integers n is n/30−n also a positive integer?  [#permalink]

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18 Mar 2019, 08:35
1
Hi Jhim123
OE
We know that $$n <30$$ or else $$30-n$$ will be negative, resulting in a negative fraction.
We also know that n> 15
or else the fraction's denominator will exceed its numerator making the fraction unable to equal a positive integer value.
Substituting all values n from 15 to 30 gives us
integer values for n=15, 20, 24, 25, 27, 28, 29.
Counting them up, we have 7
For how many positive integers n is n/30−n also a positive integer?   [#permalink] 18 Mar 2019, 08:35
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