What is the value of (2-1/3)(1+1/4)^(-1)(1+2/5)?

$$\,? = \left( {2 - {1 \over 3}} \right){\left( {1 + {1 \over 4}} \right)^{ - 1}}\left( {1 + {2 \over 5}} \right)\,\,$$
$$\left. \matrix{
2 - {1 \over 3} = {{2 \cdot 3} \over 3} - {1 \over 3} = {5 \over 3} \hfill \cr
1 + {1 \over 4} = {5 \over 4}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {1 + {1 \over 4}} \right)^{ - 1}} = {4 \over 5}\,\,\, \hfill \cr
1 + {2 \over 5} = {7 \over 5} \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = {5 \over 3} \cdot {4 \over 5} \cdot {7 \over 5} = {{4 \cdot 7} \over {3 \cdot 5}}$$

The correct answer is (D).

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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