Subject: General Aptitude · Chapter: Number System · Exam: 2009 · Marks: · Difficulty:
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
Answer (as printed):
Explanation
$\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{7}\right)+\frac{1}{n}=\frac{(21+14+6)}{42}+\frac{1}{n}=\left(\frac{41}{42}+\frac{1}{n}\right)$. This sum is a natural number when $n=42$. So, each one of the statements that 2 divides $n ; 3$ divides $n$ and 7 divides $n$ is true. Hence, $n>84$ is false.
Explanation as extracted from the printed page; notation may be imperfect.