Brent@GMATPrepNow wrote:If 40 percent more than 40 percent of x is equal to 40 percent less than y, what is the value of x/y?
A) 3/8
B) 15/16
C) 1
D) 15/14
E) 15/4
Source:
www.gmatprepnow.com
Very nice and important problem.... why nobody posted a solution till now?
I will do it step-by-step to help people who eventually tried without success...
\[? = \frac{x}{y}\,\,\,\,\,\,\,\,\left( {y \ne 0\,\,\,\,{\text{implicitly}}} \right)\]
\[40\% \,\,{\text{of}}\,\,x\,\,\, = \frac{2}{5}x\]
\[40\% \,\,{\text{more}}\,\,{\text{than}}\,\,{\text{above}} = {\text{above}} + 40\% \,\,{\text{above}} = \left( {1 + \frac{2}{5}} \right)\,\,{\text{above = }}\left( {\frac{{1 \cdot \boxed5}}{{\boxed5}} + \frac{2}{5}} \right)\,\,\left( {\frac{2}{5}x} \right) = \frac{{14}}{{25}}x\]
\[40\% \,\,{\text{less}}\,\,{\text{than}}\,\,y\,\,\, = \,\,\,60\% \,\,{\text{of}}\,\,y\,\,\, = \,\,\,\frac{3}{5}y\]
Finally,
\[\frac{{14}}{{25}}x = \frac{3}{5}y\,\,\,\,\,\,\mathop \Rightarrow \limits^{y\,\, \ne \,\,0} \,\,\,\,\,? = \frac{x}{y} = \frac{3}{5} \cdot \frac{{25}}{{14}}\, = \,\frac{{15}}{{14}}\,\,\]
Regards,
Fabio.
