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 ?
A. 2 divides n
B. 3 divides n
C. 7 divides n
D. n > 84
Answer: Option D
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
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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