If k a positive integer, is k the square of an integer?
1. k is divisible by 4.
2. k is divisible by exactly four different prime no.s
1. k is divisible by 4.
2. k is divisible by exactly four different prime no.s
K = 2 * 2 * 3 * 4 * 5 = 240; k matches statements 1 and 2, having 4 distinct prime factors and being divisible by 4, and is not a perfect square.
K = 2 * 2 * 3 * 3 * 4 * 4 * 5 * 5 is divisible by exactly 4 different primes and is divisible by 4, so is consistent with both statements. It is also equal to (2*3*4*5)^2, or 120 squared, so it is a perfect square.
Since numbers consistent with statements 1 and 2 can give us a Yes or a No answer, our answer is E, even together we don't know.
