MathRevolution wrote:
[GMAT math practice question]
If \(0.02<x<0.04\) and \(100<y<250\), which of the following could be the value of \(\frac{(y-x)}{(xy)}\)?
\(A. 10\)
\(B. 20\)
\(C. 30\)
\(D. 50\)
\(E. 100\)
\(?\,\,\,:\,\,\,\frac{{y - x}}{{xy}} = \frac{1}{x} - \frac{1}{y}\,\,\,\,\,\underline {{\text{could}}\,\,{\text{be}}}\)
\({2 \over {100}} < x < {4 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\,25 = {{100} \over 4} < {1 \over x} < {{100} \over 2} = 50\,\,\,\,\left( {\rm{I}} \right)\)
\(100 < y < 250\,\,\,\,\, \Rightarrow \,\,\,\,{1 \over {250}} < {1 \over y} < {1 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\, - {1 \over {100}} < - {1 \over y} < - {1 \over {250}}\,\,\,\,\left( {{\rm{II}}} \right)\)
\(\left( {\rm{I}} \right) + \left( {{\rm{II}}} \right)\,\,\,25 - {1 \over {100}} < {1 \over x} - {1 \over y} < 50 - {1 \over {250}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{C}} \right)\)
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net