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# If (n+12)^2 is divisible by n, where n is a natural number

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Director
Joined: 18 Jul 2018
Posts: 671
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
If (n+12)^2 is divisible by n, where n is a natural number  [#permalink]

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29 Sep 2018, 18:15
2
00:00

Difficulty:

45% (medium)

Question Stats:

53% (01:28) correct 48% (01:58) wrong based on 43 sessions

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If $$(n+12)^2$$ is divisible by n, where n is a natural number. How many values can take?

a) 4
b) 6
c) 12
d) 15
e) 22

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Intern
Joined: 22 Jun 2018
Posts: 28
Location: India
GMAT 1: 730 Q50 V39
GPA: 4
WE: Research (Telecommunications)
Re: If (n+12)^2 is divisible by n, where n is a natural number  [#permalink]

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29 Sep 2018, 18:43
2
On expansion:- (n+12)^2 = n^2 + 24n + 144

Now [n^2 + 24n + 144] /n = n + 24 + 144/n

Here = 144 = 2^4 X 3^2
Thus 144 has (4+1)( 2+1)= 15 factors.

So n can be any one of the factors of 144 to fully divide the expression.

So n can take 15 values.
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If (n+12)^2 is divisible by n, where n is a natural number  [#permalink]

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29 Sep 2018, 19:14
1
Afc0892 wrote:
If $$(n+12)^2$$ is divisible by n, where n is a natural number. How many values can take?

a) 4
b) 6
c) 12
d) 15
e) 22

$$(n+12)^2$$ is divisible by n or $$n^2+24n+144$$ is divisible by n..
n^2+24n are clearly divisible by n, so 144 also must be divisible by n..
So n can be one of the factors of 144..
$$144=12*12=2^4*3^2$$
Number of factors = (4+1)(2+1)= 5*3 = 15

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If (n+12)^2 is divisible by n, where n is a natural number   [#permalink] 29 Sep 2018, 19:14
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