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A one-million dollar inheritance was divided among five

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A one-million dollar inheritance was divided among five

by AAPL » Tue Dec 18, 2018 5:02 am

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A one-million dollar inheritance was divided among five beneficiaries. If no beneficiary received more than 30% of the inheritance, what was the greatest amount received by anyone of the beneficiaries?

1) Three of the beneficiaries received 80% of the amount received by a fourth beneficiary.
2) No beneficiary received less than 10% of the total inheritance.

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by fskilnik@GMATH » Tue Dec 18, 2018 12:49 pm

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AAPL wrote:Manhattan Prep

A one-million dollar inheritance was divided among five beneficiaries. If no beneficiary received more than 30% of the inheritance, what was the greatest amount received by anyone of the beneficiaries?

1) Three of the beneficiaries received 80% of the amount received by a fourth beneficiary.
2) No beneficiary received less than 10% of the total inheritance.
$$A \leqslant B \leqslant C \leqslant D \leqslant E\,\,\,\,\,\,\left( \$ \right)$$
$$A + B + C + D + E = {10^6}$$
$$A,B,C,D,E\,\,\,\, \leqslant \,\,\,30\% \left( {{{10}^6}} \right)$$
$$? = E$$

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {A;B;C;D;E} \right) = \left( {15\% \left( {{{10}^6}} \right);\overbrace {20\% \left( {{{10}^6}} \right);20\% \left( {{{10}^6}} \right);20\% \left( {{{10}^6}} \right);25\% \left( {{{10}^6}} \right)}^{{\rm{statement}}\,\,\left( 1 \right)}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 25\% \left( {{{10}^6}} \right) \hfill \cr
\,\,{\rm{Take}}\,\,\left( {A;B;C;D;E} \right) = \left( {\underbrace {17\% \left( {{{10}^6}} \right);17\% \left( {{{10}^6}} \right);17\% \left( {{{10}^6}} \right);21.25\% \left( {{{10}^6}} \right)}_{{\rm{statement}}\,\,\left( 1 \right)};27.75\% \left( {{{10}^6}} \right)} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 27.75\% \left( {{{10}^6}} \right) \hfill \cr} \right.$$


This solution follows 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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