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29 Sep 2018, 19:15
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Difficulty:
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Question Stats:
57% (01:45) correct
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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
a) 4
b) 6
c) 12
d) 15
e) 22
29 Sep 2018, 19:43
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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.
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.
General Discussion
29 Sep 2018, 20:14
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Afc0892
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
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
