X percent of Y percent of Z is decreased by Y percent. What is the result?

A) (100xyz - xy^2Z) / 1,000,000

B) (XZ-Y) / 100

C) (XZ-Y) / 10,000

D) (XYZ - 2Y) / 100

E) (XYZ - 2Y) / 10,000

Answer is

I don't understand on these types of problems when to solve by direct algebra or "picking numbers" as the

MGMAT book says. I calculated this probably like this:

( (x/100) * (y/100) * z ) - (y/100) = (xyz/10,000) - (y/100) = (xyz - 100y) / 10,000

MGMAT picks numbers out of thin air which I'm not the greatest at. Is there anyway to solve this with direct math?

1. \(y\) percent of \(z\) is \(\frac{y}{100}*z=\frac{yz}{100}\);

2. \(x\) percent of above value is \(\frac{x}{100}*\frac{yz}{100}=\frac{xyz}{10,000}\);

3. The above value is decreased by \(y\) percent: \(\frac{xyz}{10,000}*(1-\frac{y}{100})=\frac{xyz}{10,000}*(\frac{100-y}{100})=\frac{100xyz-xy^2z}{1,000,000}\) (for example 100 is decreased by 10 percent can be expressed as \(100*(1-\frac{10}{100})=100*(1-0.1)=100*0.9=90\)).

Answer: A.