singhmaharaj wrote:Over a certain time period, 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 shares of stocks and bonds in Ruth's portfolio increased.
2) Over the time period, the total number of shares of stocks and bonds in Ruth's portfolio increased.
Let S=10 and B=10, so that S+B = 10+10 = 20.
Statement 1: Over the time period, the ratio of the number of shares of stock to the total number of shares of stocks and bonds in Ruth's portfolio increased.
Original S/(S+B) = 10/(10+10) = 1/2.
Test one case that satisfies statement 2.
Case 1: The value of S+B increases to 30
Since new S/(S+B) must increase to a value greater than 1/2, we get:
(New S)/30 > 1/2
(New S) > 15.
Here, the value of S must INCREASE from 10 to a value greater than 15.
Test one case that doesn't satisfy statement 2.
Case 2: The value of S+B decreases to 10
Since S/(S+B) must increase to a value greater than 1/2, we get:
(New S)/10 > 1/2
(New S) > 5.
Here, the value of S could DECREASE from 10 to 6.
INSUFFICIENT.
Statement 2: Over the time period, the total number of shares of stocks and bonds in Ruth's portfolio increased.
It's possible that the value of S increases to 100, while the value of B decreases to 5.
It's possible that the value of S decreases to 5, while the value of B increases to 100.
INSUFFICIENT.
Statements combined:
As Case 1 illustrates, if the value of S+B increases, then the value of S must also increase.
SUFFICIENT.
The correct answer is
C.
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