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Last year the price per share of Stock X increased by k perc : Multiple-choice Questions — Select One Answer Choice

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Re: Last year the price per share of Stock X increased by k perc [#permalink]
1
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
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