Functions - Nova

[shanice]

For any positive integer n, pi(n) represents the number of factors of n, inclusive of 1 and itself. If a and b are prime numbers, then pi(a) + pi(b) - pi(a x b) =

a)-4 b)-2 c)0 d)-2 e)4

Solution:The only factors of a prime number are 1 and itself. Hence, pi(any prime number) = 2. So, pi(a) = 2 and pi(b) = 2, and therefore pi(a) + pi(b) = 2 + 2 = 4.

Now, the factors of ab are 1, a, b, and ab itself. Hence, the total number of factors of a x b is 4.In other words, pi(a x b) = 4.Hence, pi(a) + pi(b) - pi(a x b) = 4 - 4 = 0.

The answer is C.

My Question : Before I looked at the answer, I used different prime numbers but to no avail. However,in the solution, they use the same prime number which is 2 to solve the problem. Why? Is there something that I'm not understanding here?

Thank you.

[GMATGuruNY]

For any positive integer n, pi(n) represents the number of factors of n, inclusive of 1 and itself. If a and b are prime numbers, then pi(a) + pi(b) - pi(a x b) =

a)-4 b)-2 c)0 d)-2 e)4

Solution:The only factors of a prime number are 1 and itself. Hence, pi(any prime number) = 2. So, pi(a) = 2 and pi(b) = 2, and therefore pi(a) + pi(b) = 2 + 2 = 4.

Now, the factors of ab are 1, a, b, and ab itself. Hence, the total number of factors of a x b is 4.In other words, pi(a x b) = 4.Hence, pi(a) + pi(b) - pi(a x b) = 4 - 4 = 0.

The answer is C.

My Question : Before I looked at the answer, I used different prime numbers but to no avail. However,in the solution, they use the same prime number which is 2 to solve the problem. Why? Is there something that I'm not understanding here?

Thank you.

Let a=3 and b=5.
pi(3) = 2, since 3 has two factors (1 and 3).
pi(5) = 2, since 5 has two factors (1 and 5).
pi(3*5) = pi(15) = 4, since 15 has four factors (1,3,5,15).
Thus, pi(3) + pi(5) - pi(3*5) = 2+2-4 = 0.

The correct answer is C.

[shanice]

Thank you, Sir