Data Sufficiency

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.

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C) Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
D) EACH statement ALONE is sufficient to answer the question asked
E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed


Is the dollar amount increase is the amount increased in the share value?
For e.g : if the share value = 5 and new share value = 8 then dollar amount increase in stock is 3 ?

prachi18oct 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.

The question stem asks for the following ratio:
(rival's price today)/(telecom's original price).

Statement 1: The rival company's stock was valued at $42 per share at the beginning of last month.
After the 10% increase, the rival's price today = 42 + 10% of 42 = 46.2.
If the telecom's original price = 1, then (rival's price today)/(telecom's original price) = 46.2/1 = 46.2.
If the telecom's original price = 10, then (rival's price today)/(telecom's original price) = 46.2/10 = 4.62.
Since the ratio can be different values, INSUFFICIENT.

Statement 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.
Case 1: rival's increase = 9, telecom's decrease = 10

Since the rival's $9 increase is equal to 10% of the rival's original price -- and 9 is 10% of 90 -- the rival's original price = 90.
Thus, the rival's price today = 90+9 = 99.

Since the telecom's $10 decrease is equal to 10% of the telecom's original price -- and 10 is 10% of 100 -- the telecom's original price = 100.

Resulting ratio:
(rival's price today)/(telecom's original price) = 99/100.

Case 2: rival's increase = 90, telecom's decrease = 100
Since the rival's $90 increase is equal to 10% of the rival's original price -- and 90 is 10% of 900 -- the rival's original price = 900.
Thus, the rival's price today = 900+90 = 990.

Since the telecom's decrease of $100 is equal to 10% of the telecom's original price -- and 100 is 10% of 1000 -- the telecom's original price = 1000.
Resulting ratio:
(rival's price today)/(telecom's original price) = 990/1000 = 99/100.

Since the ratio is THE SAME in each case, SUFFICIENT.

The correct answer is B.

Answer is B.

90 %

Last month:

Our company = x
Rival = y

This month:

Our company = .9x
Rival = 1.1y

We want 1.1y / x.

S1 tells us y = 42. Doesn't give x, not sufficient.
S2 tells us .1y = .9*(.1x). This gives us x/y = .1/(.9*.1), and 1.1x/y = 1.1 * (.1/(.9*.1)). That's a value -- don't bother computing it -- so S2 is sufficient.

Answer is B

c is cost of share of first company
r is cost of share of rival company

10/100 r = 90/100 * 10/100 * c

r/c = 90/100