BTGmoderatorDC wrote:Is z equal to the median of the three positive integers, x, y, and z?
(1) x < y + z
(2) y = z
Source: GMAT Prep
\[x,y,z\,\, \geqslant 1\,\,{\text{ints}}\]
\[{\text{z}}\,\,\mathop = \limits^? \,{\text{Med}}\,\left( {x,y,z} \right)\]
\[\left( 1 \right)\,\,x < y + z\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {x,y,z} \right) = \left( {1,1,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\,{\text{Take}}\,\,\left( {x,y,z} \right) = \left( {1,2,3} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,y = z\,\,\,\, \Rightarrow \,\,\,{\text{Med}}\,\left( {x,y,z} \right) = \,\,\,{\text{Med}}\,\left( {x,z,z} \right) = z\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]
(The last equality is true if x is equal to z, and it is also true if x is not equal to z.)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
