Carcass wrote:
Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?
A. \(\frac{k}{m} %\)
B. \((k – m) %\)
C. \(\frac{100(k – m)}{(100 + k)} %\)
D. \(\frac{100(k – m)}{(100 + m)} %\)
E. \(\frac{100(k – m)}{(100 + k + m)} %\)
Let's use the INPUT-OUTPUT approach.
Another approach is to plug in values.
Let $100 be the original
price per share of Stock X
Choose a "nice" value for k. How about k =
200 So, after a
200% increase, the new price per share = $300
Let $100 be the original
earnings per share of Stock X
Choose a "nice" value for m. How about m =
100 So, after a
100% increase, the new earnings per share = $200
Original ratio of price/earnings = $100/$100 = 1
New ratio of price/earnings = $300/$200 = 1.5
By what percent did the ratio of price per share to earnings per share increase?So, the percent increase (from 1 to 1.5) is 50%.
In other words,
when k = 200 and m = 100, the ratio increases 50%Now, plug in
200 for k, and
100 for m, and look for the answer choice that also yields
50%.
A. k/m =
200/
100 =
2 (nope)
B. (k - m) =
200 -
100 =
100 (nope)
C. [100(k - m)] / (100 + k) = 10,000/300 =
33.333 (nope)
D. [100(k - m)] / (100 + m) = 10,000/200 =
50 GREAT!
E. [100(k - m)] / (100 + k + m) = 10,000/400 =
25 (nope)
Answer: D
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep