Problem Solving

BTGmoderatorDC wrote:If m > 0, y > 0, and x is m percent of 2y, then, in terms of y, m is what percent of x?

A. y/200
B. 2y
C. 50y
D. 50/y
E. 5000/y

Let y=100, implying that 2y = 200.
Let m=100.

x is m percent of 2y.
Since m=100 and 2y=200, x = 100% of 200 = 200.

m is what percent of x?
m/x = 100/200 = 1/2 = 50%. This is our target.

Now plug y=100 into the answers to see which yields the target value of 50.
Only E works:
5000/y = 5000/100 = 50.

The correct answer is E.

BTGmoderatorDC wrote:If m > 0, y > 0, and x is m percent of 2y, then, in terms of y, m is what percent of x?

A. y/200
B. 2y
C. 50y
D. 50/y
E. 5000/y
Source: Manhattan Prep

Obs.: (to our students) This is one of those problems in which we must interpret 1/2= 50% as 50 ("percent omitted") because the term "percent" is in the FOCUS.
(Don´t forget "the hidden butterfly mistake"!)

\[x = \frac{m}{{100}}\left( {2y} \right)\,\,\,\,\,\,\,\,\,\,\left[ {m,y\,\, > 0} \right]\]
\[?\,\,\,:\,\,\,\frac{m}{x} \cdot 100\left( \% \right) = f\left( y \right)\]
\[x = \frac{m}{{100}}\left( {2y} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{FOCUS}}!} \,\,\,\,\,\frac{m}{x} = \frac{{50}}{y}\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{FOCUS}}!} \,\,\,\,\,?\,\, = \,\,\frac{m}{x} \cdot 100\left( \% \right) = \frac{{50}}{y} \cdot 100\left( \% \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left( E \right)\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.