Percents

To find: Number of stock increased?

Statement 1:
stock : (stock + bond) = increased
We dont know whether bonds decreased..
INSUFFICIENT
INSUFFICIENT

Statement 2:
stock + bond ==> increased
We dont know what increased
INSUFFICIENT

combining..
stock : (stock + bond) = increased
stock + bonds = increased
since, the denominator has increased.. also the ratio has increased.. this is only possible when numerator has also increased.
So, stocks must have increased.
SUFFICIENT

[spoiler]{C}[/spoiler]

The first statement does not say stock : bond ==> increased instead it says stock : (bond + stock) ===> increased

singhmaharaj wrote:The first statement does not say stock : bond ==> increased instead it says stock : (bond + stock) ===> increased

Ah sorry!.. Corrected my Solution

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.