Over a certain time period, did the number of shares of stock in Ruth'

Over a certain time period, did the number of shares of stock in Ruth's portfolio increase?

Let the # of stock be \(s\) and the # of bonds be \(b\). The question is did \(s\) increase?

(1) Over the time period, the ratio of number of shares of stock to the total number of shares of stocks and bonds in Ruth's portfolio increased. \(\frac{s}{s+b}\) increased. Not sufficient, as for example it's possible that \(s\) increased \(b\) remained the same or \(s\) remained the same and \(b\) decreased.

(2) Over the time period, the total number of shares of stocks and bonds in Ruth's portfolio increased. \(s+b\) increased. Clearly insufficient.

(1)+(2) \(\frac{s}{s+b}\) increased and \(s+b\) (denominator) also increased, so it must be true that \(s\) (nominator) increased too. Sufficient.

Answer: C.

Hope it's clear.