EgmatQuantExpert wrote:

Anna wants to distribute chocolates among her four children in the ratio \(\frac{1}{2} : \frac{1}{5} : \frac{1}{6} : \frac{1}{12}\). How many minimum chocolates should she buy, so that she can distribute the chocolates in the given ratio?

a. 30

b. 45

c. 57

d. 90

e. 120

\(? = \min \left( {{\rm{Total}}} \right)\)

\({1 \over 2}\,\,:\,\,{1 \over 5}\,\,:\,\,{1 \over 6}\,\,:\,\,{1 \over {12}}\,\,\,\,\mathop \Leftrightarrow \limits_{:\,\,60}^{ \cdot \,\,60} \,\,\,\,30:12:10:5\)

\(\left\{ \matrix{

{\rm{Child}}\,1 = 30k \hfill \cr

{\rm{Child}}\,2 = 12k \hfill \cr

{\rm{Child}}\,3 = 10k \hfill \cr

{\rm{Child}}\,4 = 5k \hfill \cr} \right.\,\,\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,Total = 57k\,\,\,\,\,\,\mathop \Rightarrow \limits^{k\,\,{\mathop{\rm int}} \,\,\left( * \right)} \,\,\,\,\,\,? = \min \,\,\left( {{\rm{Total}}} \right)\,\,\, = \,\,57 \cdot 1 = 57\)

\(\left( * \right)\,\,\,\,\left\{ \matrix{

5k\,\, = {\mathop{\rm int}} \hfill \cr

2k = 12k - 10k\,\, = \,\,{\mathop{\rm int}} - {\mathop{\rm int}} = {\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,k = 5k - 2 \cdot \left( {2k} \right) = {\mathop{\rm int}} - 2 \cdot {\mathop{\rm int}} = {\mathop{\rm int}}\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)

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