M01-26

Official Solution:


If \(x\) is a positive integer, then is \(x\) a prime number?

(1) \(x\) is a multiple of a prime number.

If \(x=2\), then the answer is YES, as every integer is a multiple of itself. However, if \(x=4\), the answer is Not Sufficient.

(2) \(x=a*b\), where \(a\) and \(b\) are different integers.

Any integer greater than 1 can indeed be expressed as the product of two different integers. For instance, \(x=2\) (which is prime) can be written as \(1*2\), and \(x=4\) (which is not prime) can be written as \(1*4\). Not sufficient.

(1)+(2) From (2) we deduce that \(x\) is not 1, but this does not help us determine whether \(x\) is prime. For example, if \(x=2\), the answer would be YES, but if \(x=4\), the answer would be NO. Not sufficient.


Answer: E