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For any positive integer n, \(\pi(n)\) represents the number of factors of n, inclusive of 1 and itself. a and b are prime numbers

Quantity A

Quantity B

\(\pi(a) + \pi(b)\)

\(\pi(a * b)\)

A. The quantity in Column A is greater B. The quantity in Column B is greater C. The two quantities are equal D. The relationship cannot be determined from the information given

Re: For any positive integer n, π(n) represents the number of fa [#permalink]
04 Apr 2018, 15:43

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Answer: C (DOUBTS) A: P(a) + P(b) The only factors of a prime number are 1 and the number itself. So P(a) + P(b) always equals 2+2 = 4

B: P(a*b) The factors of a*b are 1, a, b, a*b. Why not more than 4? Because no new divider is produced with multiplying a to b. If there were any it was a factor of a or b (a factor other than a and b themselves and a) and thus a or b couldn’t be prime. So factors of a*b are 4 numbers. For example if a = 3 and b = 11 then P(a*b) = P(33) = 4 (1, 3, 11, 33)

A and B are both 4 and equal. The answer is C. _________________