# NMTC doubt questions

I recently appeared nmtc final round junior and these are the questions in which i have doubt. Please upload the solution if you know the answer
Q.1 a,b,c are positive real numbers. Find the minimum value of $$\frac{a+3c}{a+2b+c}$$+ $$\frac{4b}{a+b+2c}$$- $$\frac{8c}{a+b+3c}$$ I got the answer $$\frac{2}{5}$$ . Is it correct?

Q.2 show that for any natural number n, there is a positive integer all of whose digits are 5 or 0 and is divisible by n. I have totally no idea how this one is done , and i ended up just bluffing some answer in the end. thanks in advance for the solution

Note by Sayantan Dhar
1 year, 7 months ago

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Question 1: The minimum value is $$12\sqrt2 - 17$$ and it occurs when $$(a,b,c) = \left( \dfrac32 - \sqrt2, \dfrac1{\sqrt2} - \dfrac12 , \dfrac1{\sqrt2} \right)$$.

- 1 year, 7 months ago

can you please post the detailed solution

- 1 year, 7 months ago