BTGmoderatorDC wrote:For any integers a, b, c, and d, sechigh(a, b, c, d) is the second highest integer when the integers are placed in an ordered list. For example sechigh(2, 5, 4, 6) = 5 and sechigh(6, 5, 3, 6) = 6 . For the integer y, what is the value of sechigh(6, 7, 11, y)?
(1) y = sechigh (7, 13, 12, x) for some integer x.
(2) y = sechigh (7, 13, 8, z) for some integer z.
Source: Manhattan Prep
$$? = {\rm{sechigh}}\left( {6,7,11,y} \right)\,\,\,\,\,\,\,\,\left[ {y\,\,{\mathop{\rm int}} } \right]$$
$$\left( 1 \right)\,\,y = {\rm{sechigh}}\left( {7,13,12,x} \right)\,\,\,\,\left[ {x\,\,{\mathop{\rm int}} } \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{
\,y = 13\,\,\,{\rm{if}}\,\,\,x \ge 13\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 11 \hfill \cr
\,y = 12\,\,\,{\rm{if}}\,\,\,x \le 12\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 11 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,y = {\rm{sechigh}}\left( {7,13,8,z} \right)\,\,\,\,\left[ {z\,\,{\mathop{\rm int}} } \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,z = 7\,\,\,\,\, \Rightarrow \,\,\,\,\,y = 8\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 8 \hfill \cr
\,\,{\rm{Take}}\,\,z = 14\,\,\,\,\, \Rightarrow \,\,\,\,\,y = 13\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 11 \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
