The product of two negative integers, a and b, is a prime number p. If p is the number of factors of n, where n is NOT a perfect square, what is the value of the median of the four integers a, b, p, and n?
Choose the correct choice from the following options:
A) 0
B) 1/2
C) 1
D) 3/2
E) 2
All prime numbers are divisible by 1 and itself. now since product of a and b is a prime number P. therefore one of a and b is -1 and other is -P.   Also, all the perfect square have odd no. of factors. for e.g. a^2 will have 3 factors a,a^2 and 1. Since, n is not a perfect square therefore its no. of factors must be even and the only prime no. which is even is 2. therefore p=2,   now the median of numbers -2,-1,2 and n will be (-1+2)/2= 1/2   ANSWER:1/2
<result>B</result>
The product of two negative integers, a and b, is a prime number p. If p is the number of factors of n, where n is NOT a perfect square, what is the value of the median of the four integers a, b, p, and n?