BTGmoderatorDC wrote:The price per share of stock X increased by 10 percent over the same time period that the price per share of stock Y decreased by 10 percent. The reduced price per share of stock Y was what percent of the original price per share of stock X?
(1) The increased price per share of stock X was equal to the original price per share of stock Y
(2) The increase in the price per share of stock X was 10/11 the decrease in the price per share of stock Y
Source: Official Guide
In our method we make a
clear distinction between Problem Solving and Data Sufficiency.
In Data Sufficiency problems, we are
FOCUSED in the UNIQUENESS OR NOT of a (numerical) value, not in calculations related to the possible value(s)...
Read our solution, that starts below, with that in mind!
\[\left( {{\text{DATA}}} \right)\,\,\,\,X\,\,\, \to \,\,\,\frac{{11}}{{10}}X\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,Y\,\,\, \to \,\,\,\frac{9}{{10}}Y\]
\[\left( {{\text{FOCUS}}} \right)\,\,\,\,? = \frac{{\,\frac{9}{{10}}Y\,}}{X}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{? = \frac{Y}{X}}\,\,\,\,\,\,\,\,\,\,\,\left( {X \ne 0\,\,\,\,{\text{implicitly}}} \right)\]
\[\left( 1 \right)\,\,\,\frac{{11}}{{10}}X = Y\,\,\,\, \Rightarrow \,\,\,\,\,\frac{Y}{X}\,\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]
\[\left( 2 \right)\,\,\,\frac{1}{{10}}X = \frac{{10}}{{11}}\left( {\frac{1}{{10}}Y} \right)\,\,\,\, \Rightarrow \,\,\,\,\,\frac{Y}{X}\,\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\]
(If you realize this is BRUTAL, SAFE and POWERFUL, you understood correctly. )
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
