NMTC 2015

Number Theory Level 2

The smallest natural number ′ n ′ 'n' which satisfies 1 2 200 < n 300 12^{200}<n^{300} is:

Source : NMTC 2015 Inter Level.


The answer is 6.

Shivam Jadhav by Shivam Jadhav , 22, India

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2 solutions

Aditya Chauhan
Aug 25, 2015

1 2 200 < n 300 12^{200} < n^{300}

On taking the 100th root we get

1 2 2 < n 3 12^{2} < n^{3}

144 < n 3 144 < n^{3}

Smallest value that satisfies this is 6 \boxed{6}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

@Aditya Chauhan Looks like we posted our solutions at the same time :P

Mehul Arora - 5 years, 9 months ago
Mehul Arora
Aug 25, 2015

Taking 100th root on both sides

1 2 2 < n 3 12^2 < n^3

m i n ( x ) = 6 min (x) =6

2 Helpful 0 Interesting 0 Brilliant 0 Confused

@Shivam Jadhav Please stop using \ [.......... \ ] everywhere. They're frustrating to read.

Mehul Arora - 5 years, 9 months ago

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