pemdas wrote:GmatMathPro, thanks for intro with Boyle's however this question specifies different conditions
two functions are given with three values, two are variable and one is const.
you have made all three variables in one function
But doesn't it bother you at all that none of your data even comes close to satisfying your original equations?
You say x=z/y^2. The given data is x=16, y=2, z=4. Plugging this into your equation, you get 16=4/2^2 or 16=1. Then at the end you say when y=4 and z=25, then x=256. Plugging this in to this equation gives you 256=25/16.
Your other equation is x=y√z. Plugging in the first set of data gives 16=2√4 or 16=4. Plugging in your second set of data gives 256=4√25 or 256=20.
Meanwhile, my equation, x=32√z/y^2, for x=16, y=2, z=4 gives 16=32√4/2^2 or 16=16. My second set of data is x=10, y=4, z=25. Plugging in to my equation gives 10=32√25/4^2 or 10=10.
Also, it doesn't say that z is a constant, it says "when z is constant", and it doesn't say that y is a constant, it says "when y is constant". That is, y and z are variables, but certain relationships are true when each of these variables is held constant. For instance, let's say z is held constant at some specific value, then in my equation, x=32√z/y^2, 32√z will always be the same number, because we are holding z constant. Let's call that number A. So A=32√z, and the equation becomes x=A/y^2. In words, when is z held constant, x varies inversely with y^2. Now, when y is held constant at some specific value, 32/y^2 will always be the same number. Let's call it B. So the equation becomes x=B√z. In words, when y is held constant, x varies directly as the square root of z.
