In the equality above, A,B,C are positive integers. What is

$$A,B,C\,\, \ge 1\,\,\,{\rm{ints}}\,\,\,\left( * \right)$$
$${{71} \over {11}} = A + {1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}}$$
$$? = 2A + 3B - 4C$$

$$\left. \matrix{
B + {1 \over {C + 1}}\,\,\mathop > \limits^{\left( * \right)} \,\,1\,\,\,\,\, \Rightarrow \,\,\,\,\,0 < \,{1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}} < 1\,\,\,\, \hfill \cr
{{71} \over {11}} = {{66 + 5} \over {11}} = 6 + {5 \over {11}} \hfill \cr} \right\}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,A = 6$$
$$\left. \matrix{
{5 \over {11}} = {1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,B + {1 \over {C + 1}}\,\, = {{11} \over 5}\,\,\, \hfill \cr
C + 1\,\,\mathop > \limits^{\left( * \right)} \,\,1\,\,\,\, \Rightarrow \,\,\,\,\,0 < {1 \over {C + 1}} < 1 \hfill \cr
{{11} \over 5} = {{10 + 1} \over 5} = 2 + {1 \over 5} \hfill \cr} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,B = 2$$

$${1 \over 5} = {1 \over {C + 1}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,C = 4$$

$$? = 2\left( 6 \right) + 3\left( 2 \right) - 4\left( 4 \right) = 2$$

The correct answer is (C).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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In the equality above, A,B,C are positive integers. What is

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