CAT Quant Practice Problems

Question: For real numbers x and y, let

\(f\left( {x,y} \right) = \left\{ \begin{array}{l}{\rm{Positive\; square\; root \;of\; }}\left( {x + y} \right),{\rm{if }}{\left( {x + y} \right)^{0.5}}{\rm{\; is\; real}}\\{\left( {x + y} \right)^2},{\rm{ otherwise}}\end{array} \right.\)

\(g\left( {x,y} \right) = \left\{ \begin{array}{l}{\left( {x + y} \right)^2},{\rm{ if }}{\left( {x + y} \right)^{0.5}}{\rm{\; is\; real}}\\ - \left( {x + y} \right),{\rm{ otherwise}}\end{array} \right.\)

Which of the following expressions yields a positive value for every pair of non-zero real numbers (x, y)?

f(x, y) – g(x, y)
f(x, y) – (g(x, y))2
g(x, y) – (f(x, y))2
f(x, y) + g(x, y)
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