I3igDmsu wrote:

Beth and Jim each received a salary increase. If Jim's salary was increased by the same percent as Beth's salary, did Beth receive a greater dollar increase in salary than Jim?

(1) Before the increases, Jim's salary was greater than $25,000.

(2) Before the increases, Jim's salary was 4/5 of Beth's salary.

\(B,J\,\, > 0\,\,\,\,\left[ \$ \right]\,\,\,\,\,\left\{ \matrix{

\,B \to \left( {1 + x} \right)B \hfill \cr

\,J \to \left( {1 + x} \right)J \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\left( {{\rm{increase}}:\,\,x\,\,\left( \% \right)\,\, > 0} \right)\)

\(xB\mathop > \limits^? xJ\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{x\, > \,0} \,\,\,\,\,\,\boxed{\,\,B\mathop > \limits^? J\,\,}\,\)

\(\left( 1 \right)\,\,\,\,J > 25000\,\,\,\left\{ \matrix{

\,{\rm{Take}}\,\,\left( {B,J} \right) = \left( {26000,26000} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr

\,{\rm{Take}}\,\,\left( {B,J} \right) = \left( {27000,26000} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\)

\(\left( 2 \right)\,\,J = {4 \over 5}B\,\,\mathop < \limits^{B\, > \,\,0} \,\,B\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle\)

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

Regards,

Fabio.

_________________

Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)

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