Let X be the company whose stock increased by 10% (the rival), and Y be the other. Now suppose the stock prices started at 100x and 100y.

X's stock price went up 10% from 100x to 110x
Y's stock price dropped 10% from 100y to 90y

Y's value today (90y) is what percentage of X's value last month (100x)? We're asked for 90y/100x. Since we know what 90/100 is, we can rephrase the question to: what is y/x ?

Statement 1:
100x = 42. This gives us no ratio information. INSUFFICIENT

Statement 2:
X's increase (110x-100x= 10x) was 90% as much as Y's decrease (100y-90y= 10y). So 10x is 90% of 10y. 10x/10y = 90/100. From this we can find x/y and invert that to get y/x. Thus we can definitively answer our rephrase. SUFFICIENT

The answer is B

[email protected] wrote:A telecommunications company's stock fell 10% last month, while a rival company's stock increased by 10%. The rival company's stock value today is what percentage of the telecommunication company's stock value at the beginning of last month?

(1) The rival company's stock was valued at $42 per share at the beginning of last month.

(2) The dollar amount of the rival company's stock increase was 90% as much as the dollar amount of the decrease in the telecommunication company's stock.

If we let the stock value of the rival company at the beginning of last month = x, and the stock value of the telecommunications company at the beginning of last month = y, then we can represent the current value of the rival company's stock as 1.1x (i.e., with an increase of 0.1x in value) and the current value of the telecommunications company's stock as 0.9y (with a decrease of 0.1y in value).

We need to determine what percentage the rival company's stock value today is of the telecommunications company's stock value at the beginning of last month. That is:

(1.1x)/y = ?

Statement One Alone:

The rival company's stock was valued at $42 per share at the beginning of last month.

We know that x = 42; however, without knowing any information regarding the other company, we cannot answer the question. Statement one alone is not sufficient.

Statement Two Alone:

The dollar amount of the rival company's stock increase was 90% as much as the dollar amount of the decrease in the telecommunication company's stock.

Using the information in statement two, we can create the following equation:

0.1x = 0.9(0.1y)

x = 0.9y

x/y = 0.9

Since we have a value for x/y, statement two alone is sufficient.

Answer: B