k a positive integer

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.

KapTeacherEli wrote: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.

Statement 2 says:"exactly 4 different primes"
doesn't it mean that k may consist prime no.s only once , i mean k=2x3x5x7 and not k=2x2x3x5x7 ?

vaibhav.iit2002 wrote:
Statement 2 says:"exactly 4 different primes"
doesn't it mean that k may consist prime no.s only once , i mean k=2x3x5x7 and not k=2x2x3x5x7 ?

K is divisble by exactly four primes--2, 3, 5, and 7. That doesn't meant it has exactly four prime facotrs; that's not the same thing. Further, if it WAS 2x3x5x7, it couldn't be divisible by 4. Remember, DS statements never conflict.