Explanation

Translate what you are told into algebra: $\frac{x}{y}=2$ and $x=\frac{75}{100}\times z=\frac{3}{4}\times z$.

Notice that the problem then tells you that z is larger than w, not z is of $\frac{3}{4}$ w.

That means $z=w+\frac{3}{4}w=(1+\frac{3}{4})w=\frac{7}{4}w$.

At this point, you can either Plug In or do algebra.

To Plug In, choose 4 for w, so z = 7, and $x=\frac{3}{4}\times 7=\frac{21}{4}$.

If $\frac{x}{y}=2$, then x = 2y, so $\frac{21}{4}=2y$; $y= \frac{21}{8}$.

Now plug $\frac{21}{8}$ into the answer choices for y to see which hits your target number, w = 4.

Only choice (C) does. Alternatively, to do algebra, combine the first two equations you translated into algebra: $2y=\frac{3}{4} z$; $z=\frac{8}{3}$.

Combining this equation with the one you derived above, it follows that $\frac{8}{3}y= \frac{7}{4}w$, and $w= \frac{32}{21}y$; the answer is choice (C).