Rudy414 wrote:If x is even, and 90 ≤ x ≤ 100, what is the value of x?

1) x and x/2 have the same distinct prime factors
2) x/2 has two prime factors

Possible values of x are : 90, 92, 94, 96, 98, and 100

Statement 1: This means x must be divisible by 4
Hence, possible values of x are : 92, 96, and 100

Not sufficient

Statement 2: Possible values of x/2 are : 45, 46, 47, 48, 49, and 50
Now,

• 45 = 3*3*5
  46 = 2*23
  47 = 47
  48 = 2*2*2*2*3
  49 = 7*7
  50 = 2*5*5

As x/2 has two prime factors, possible values of x/2 are : 46 and 49
Hence, possible values of x are : 92 and 98

Not sufficient

1 & 2 Together: Only possible value of x is 92

Sufficient

The correct answer is C.

Rudy414 wrote:For statement 1, can you explain why x must be divisible by 4? I don't quite understand how you reached that conclusion.

As x is even, let us assume that x = 2*a*b*c*..., where a, b, c etc are prime factors of x.
So, x/2 = a*b*c*...

As x and x/2 have same distinct prime factors and 2 is a prime factor of x, 2 must be a prime factor of x/2 also. Hence, at least one of a, b, c etc must be equal to 2. Which in turn means x will be divisible by another 2, i.e. x is divisible by 4.

Hope that helps.