rsarashi wrote:Of the shares of stock owned by certain investor, 30 percent are share of company X stock and 1/7 of the remaining shares are shares of company Y stock. How many shares of company X stock does the investor own?
|) The investors owns 100 shares of company Y stock.
||) The investor owns 200 more shares of company X stock than of company Y stock.
OAD
We can let n = the total number of shares, x = the number of company X shares, and y = the number of company Y shares, and we can create the following equations:
0.3n = x
and
(1/7)(0.7)n = y
(1/7)(7/10)n = y
(1/10)n = y
If we can produce a third unique equation with one or more of the variables n, x, or y, or if we know one of the two values of n and y, we can determine the value of x.
Statement One Alone:
The investors owns 100 shares of company Y stock.
Since y = 100, we see that we can determine x. Statement one alone is sufficient to answer the question.
Statement Two Alone:
The investor owns 200 more shares of company X stock than of company Y stock.
We have:
y = 200 + x
Since we have a third unique equation, statement two alone is sufficient to answer the question.
If this is not obvious to you, here is an alternate explanation: In the equation y = 200 + x, we can substitute 0.3n for x and we can substitute 0.10n for y, yielding:
0.10n = 200 + 0.3n
At this point, we see that we can easily solve for n, and then for x.
Answer:
D
