fskilnik wrote:
GMATH practice exercise (Quant Class 14)
If \(G\) is a function defined in the positive integers, such that \(G(k)\) is a positive integer for each positive integer \(k\), what is the value of \(G(G(2019))\) ?
(1) \(G(G(m+n)) = m+n\) , for every positive integers \(m,n\).
(2) \(G(n) = m\) implies \(G(m) = n\), for every positive integers \(m,n\).
\(? = G\left( {G\left( {2019} \right)} \right)\)
\(\left( 1 \right)\,\,\,\left\{ \matrix{\\
\,G\left( {G\left( {m + n} \right)} \right) = m + n\,\,\,\left( {m,n \ge 1\,\,{\rm{ints}}} \right) \hfill \cr \\
\,\,\,\,\,\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2018,1} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\, = \,\,G\left( {G\left( {2018 + 1} \right)} \right)\,\, = \,\,2018 + 1\,\, = \,\,2019\)
\(\left( 2 \right)\,\,\,G\left( n \right) = m\,\,\,\, \Rightarrow \,\,\,\,\,G\left( m \right) = n\,\,\,\,\left( {m,n \ge 1\,\,{\rm{ints}}} \right)\,\,\,\,\,\left( * \right)\,\)
\({\rm{Take}}\,\,\left( {n,m} \right) = \left( {2019,G\left( {2019} \right)} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,? = G\left( {G\left( {2019} \right)} \right) = 2019\)
The correct answer is (D).
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)