Let n be a natural number such that $$\frac{1}{2}$$ + $$\frac{1}{3}$$ + $$\frac{1}{7}$$ + $$\frac{1}{n}$$   is also a natural number. Which of the following statements is not true ?

Solution (By Examveda Team)

$$\eqalign{ & = \left( {\frac{1}{2} + \frac{1}{3} + \frac{1}{7}} \right) + \frac{1}{n} \cr & = \frac{{\left( {21 + 14 + 6} \right)}}{{42}} + \frac{1}{n} \cr & = \left( {\frac{1}{{42}} + \frac{1}{n}} \right) \cr} $$
This sum is a natural number when n = 42
So, each one of the statements that 2 divides ; 3 divides n and 7 divides n is true.
Hence, n > 84 is false