Data Sufficiency

Princeton Review

A father distributed his total wealth to his two sons. How much wealth did the father have?

1) The elder son received 3/5 of the wealth.
2) The younger son received $30,000.

OA C

AAPL wrote:Princeton Review

A father distributed his total wealth to his two sons. How much wealth did the father have?

1) The elder son received 3/5 of the wealth.
2) The younger son received $30,000.

All numbers are in thousands of dollars.
$$? = W$$
$$\left( {Y\, = \,\,{\text{younger}}\,\,{\text{part}}\,\,{\text{,}}\,\,\,E = {\text{elder}}\,\,{\text{part}}} \right)$$
$$\left( 1 \right)\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {30,45} \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = 75\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {20,30} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 50\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\left\{ \matrix{
\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {30,45} \right)\,\,\,\,\, \Rightarrow \,\,\,? = 75\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {30,40} \right)\,\,\,\,\, \Rightarrow \,\,\,? = 70\,\, \hfill \cr} \right.\,$$
$$\left( {1 + 2} \right)\,\,\,30 = Y = \frac{2}{5}\left( W \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = W = 75$$

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

Regards,
Fabio.

Statement 1
The elderly son received 3/5 of the wealth. We don't know the total wealth so we can't find the 3/5 of the total wealth.
Hence statement 1 is INSUFFICIENT.

Statement 2
The younger son received 30,00 dollar
Total wealth = younger son's share + Elderly son's share
We don't know the elderly son's share, hence statement 2 is INSUFFICIENT.

Combine statement 1 and 2 together
Elder son received 3/5 hence younger son's share = 2/5

Younger son received 30,000 dollars, hence
2/5 of his total wealth = 30,000 dollars
let total wealth=w
$$\frac{2}{5}\cdot w=30,000$$
$$w=\frac{30000}{\frac{2}{5}}$$
$$w=75,000\ dollars$$
Two statements combined together are SUFFICIENT.
$$answer\ is\ option\ C$$