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.
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I chose A...but it isnt the correct answer.
Logic :
(#of shares of stocks/Tot shares+bonds)-->increases
Hence number of shares of stocks would have a direct dependency, hence it increase as well.

i vvonder vvhat is really the concept being tested here ..

I think maybe "How to compare two fractions"?

(1) For example, \(S/(S+B)\) can increase if S increases and B stays the same, but also if S stays the same and B decreases (she can sell some bonds).
Therefore, (1) is not sufficient.

(2) Obviously, not sufficient. S+B can also increase by increasing B, while S stays the same.

(1) and (2) together: We have to compare \(\frac{S_1}{S_1+B_1}\) to \(\frac{S_2}{S_2+B_2}\). If \(S_2+B_2 > S_1+B_1\) (the total number increased), then to have the second fraction larger than the first we need a larger \(S_2\), or increase in S. Otherwise, the second fraction is going to be smaller, because it has a larger denominator.

Answer, definitely C.
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1) The ratio of shares:total could increase by adding more shares or by reducing the number of bonds. Insufficient.

2) The total number could increase by adding shares, adding bonds, or both. Insufficient.

Combined, we know the total number of shares and bonds went up, and we know the ratio of shares:total went up. The only way both statements can be true is if the number of shares increased. Thus, we need both statements.
Hence C.
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Even I did the question with the same logic, since the ratio is increasing so either only numerator increases or both numr and denomr should be increasing.

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