The "spin" of any two-digit number is defined as double the amount of

This one is going to be all about translating the question into plain English. When is the spin of a number divisible by 4? When twice the tens digit is divisible by 4.

When will that happen? Well, if you double an even number, it's divisible by 4. If you double an odd number, it isn't. So, the question is really asking: 'is the tens digit of X even?'

Statement 1: We don't know whether the tens digit of x is even or odd. Insufficient.

Statement 2: We don't know whether the tens digit of x is even or odd. Insufficient.

Both statements together: I'm pretty sure this will still be insufficient, but at this point I'd want to check with specific cases, just to be totally sure. For a number to fit both statements, its tens digit should be 5 or higher (to make it bigger than 50), and the ones digit should be 9 minus the tens digit.

Two numbers that work are 54 and 63. 54 has an odd tens digit, and 63 has an even tens digit. Since we can get both results, the statements are still insufficient together.

The correct answer is E.