ST wrote:Over a certain time period, did the number of shares in Ruth's portfolio increase?
1) Over the time period, the ratio of hte number of shares of stock to the total number of shares of stocks and bonds in Ruth's portfolic increased.
2) Over the time period, the total number of shared of stocks and bonds in Ruth's portfolio increased.
can anyone explain why answer is C?
First, we need to clear up some ambiguities. Here's what's unclear:
- what does "shares" mean? Does it refer only to stocks, or are there other types of shares?
- is it "shares of (stocks and bonds)" or "(shares of stocks) and bonds"?
Let's rewrite the question to make it unambiguous:
Over a certain period of time, did the number of shares of stock in Ruth's portfolio increase?
(1) Over the time period, the ratio of the number of shares of stock to the total number of bonds and shares of stock in Ruth's portfolic increased.
(2) Over the time period, the total number of bonds and shares of stock in Ruth's portfolio increased.
1) there are two ways to increase a ratio: increase the numerator and decrease the denominator.
From (1), we know that either #stocks went up OR #bonds went down. So, the # of shares of stocks could have gone up, but we don't know for sure: insufficient.
2) tells us nothing about stocks and bonds individually: insufficient.
Together: if the entire S/(S+B) ratio went up AND the denominator (S+B) went up, then the numerator must have also increased. Together, we know that the number of shares of stock increased: sufficient, choose (C).
