If the least common multiple of 2x and y is 400 and the greatest commo

If the least common multiple of 2x and y is 400, then if we multiply 2x and y each by 3, the resulting values will have a least common multiple of 1200.
In other words, the least common multiple of 6x and 3y is 1200

We're also told that the greatest common divisor of 6x and 3y is 30

--------ASIDE----------------------
There's a nice property that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xy
Example: x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------

When we apply the above property, we get: (GCD of 6x and 3y)(LCM of 6x and 3y) = (6x)(3y)
Substitute values to get: (30)(1200) = (6x)(3y)
Simplify to get: 36,000 = 18xy
Divide both sides by 18 to get: 2000 = xy

So, \(\frac{xy}{2}=\frac{2000}{2} = 1000\)

Answer: C