Suppose a, b and c are three distinct natural numbers such that a + b + c = abc. Consider the following statements : 1. The arithmetic mean of a, b and c is a natural number. 2. The harmonic mean of a, b and c lies between 1 and 2. Which of the statements

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Q: 98 (CAPF/2023)
Suppose a, b and c are three distinct natural
numbers such that a + b + c = abc.
Consider the following statements :
1. The arithmetic mean of a, b and c is a
natural number.
2. The harmonic mean of a, b and c lies
between 1 and 2.
Which of the statements given above is/are
correct?

question_subject: 

Mathematics

question_exam: 

CAPF

For the given condition a + b + c = abc, calculating the arithmetic mean (a+b+c)/3 is usually not an integer unless the numbers are specifically chosen in a such way, not true for general distinct numbers. However, the harmonic mean, given by 3abc/(ab + bc + ca) for these, can lie between 1 and 2, demonstrating that only statement 2 can be concluded true in a specific solve.