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# For how many integers n is n/(20 - n) the square of an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 59589
For how many integers n is n/(20 - n) the square of an integer?  [#permalink]

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19 Mar 2019, 01:12
00:00

Difficulty:

95% (hard)

Question Stats:

14% (01:44) correct 86% (01:51) wrong based on 29 sessions

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For how many integers n is $$\frac {n}{20-n}$$ the square of an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 10

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5436
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: For how many integers n is n/(20 - n) the square of an integer?  [#permalink]

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19 Mar 2019, 05:04
Bunuel wrote:
For how many integers n is $$\frac {n}{20-n}$$ the square of an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 10

N=20X^2/X^2+1
x^2=0,1,2,3 ; x^2 +1 is divisible by 4 factors
total 4 factors
IMO D
Senior Manager
Joined: 12 Sep 2017
Posts: 308
Re: For how many integers n is n/(20 - n) the square of an integer?  [#permalink]

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19 Mar 2019, 15:03
Archit3110 wrote:
Bunuel wrote:
For how many integers n is $$\frac {n}{20-n}$$ the square of an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 10

N=20X^2/X2+1
x^2=0,1,2,3 ; x^2 +1 is divisible by 4 factors
total 4 factors
IMO D

Hello Archit3110!

Could you please give a more detailed explanation.

Why are you multiplying 20*x^2?

Kind regards!
Re: For how many integers n is n/(20 - n) the square of an integer?   [#permalink] 19 Mar 2019, 15:03
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