ideree 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) k% / m
(B) (k - m)%
(C) 100(km) % / 100+k
(D) 100(k − m) % / 100+m
(E) 100(k − m) % / 100+k +m
Original ratio:
Let the original price = 1 and the original earnings = 1.
Resulting ratio:
price/earnings = 1/1 = 1.
New ratio:
Let k=200 and m=100.
Since the price increases by k=200%, the new price = 1 + (200/100)(100) = 3.
Since the earnings increase by m=100%, the new earnings = 1 + (100/100) = 2.
Resulting ratio:
(new price)/(new earnings) = 3/2 = 1.5.
Since the old ratio = 1 and the new ratio = 1.5, the ratio increases by 50%. This is our target.
Now plug k=200 and m=100 into the answers to see which yields our target of 50.
Only
D works:
100(k-m)/(100+m) = (100)(200-100) / (100+100) = 50.
The correct answer is
D.
An alternate approach is to combine plugging in values with a bit of algebra.
Old ratio:
Let the original price = 100 and the original earnings = 1--.
Original ratio of price to earnings = 100/100 = 1.
New ratio:
Price increased by k% = 100 + (k/100)(100) = 1 + k.
Earnings increased by m% = 1 + (m/100)(100) = 100 + m.
New ratio = (100+k)/(100+m).
Difference between the ratios:
(100+k)/(100+m) - 1 = [(100+k) - (100+m)] / (100+m) = (k-m)/(100+m).
Percent change in the ratios = (difference between the ratios)/(original ratio) * 100:
[(k-m)/(100+m)] / 1 * 100 = [100(k-m)] / (100+m).
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
