Last year the price per share of Stock X increased

[rsarashi]

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(k - m)] / (100 + k) %
D. [100(k - m)] / (100 + m) %
E. [100(k - m)] / (100 + k + m) %

OAD

[Brent@GMATPrepNow]

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(k-m)/100+k %
D) 100(k-m)/100+m %
E) 100(k-m)/100+k+m %

One 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

[DavidG@VeritasPrep]

It's worth noting that on these types of questions, the correct answers seem to be disproportionately weighted towards D and E. (At least they are in the Official Guide - most test-takers will start with A and work their way down, so if the correct answer is D or E, the problem is more time consuming.) When I'm picking numbers, I like to start with E and work my way up.

[GMATGuruNY]

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(k - m)] / (100 + k) %
D. [100(k - m)] / (100 + m) %
E. [100(k - m)] / (100 + k + m) %

OAD

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 = 100.
Original ratio of price to earnings = 100/100 = 1.

New ratio:
Price increased by k% = 100 + (k/100)(100) = 100 + k.
Earnings increased by m% = 100 + (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.

[Scott@TargetTestPrep]

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(k - m)] / (100 + k) %
D. [100(k - m)] / (100 + m) %
E. [100(k - m)] / (100 + k + m) %

OAD

Solution:

We can choose convenient numbers for the original stock price and its earnings. We can also choose convenient numbers for k and m, keeping in mind that m < k.

We can let the original price of stock X be $200; thus, its price increased by 20% to $240 (notice that k = 20). Similarly, we can let the original earnings of stock X be $100and we let the earnings increase by 10% to $110 (notice that m = 10). We see that the original ratio of price to earnings ratio is 200/100 = 2 and the new ratio is 240/110 = 24/11. Therefore, the ratio is increased by:

(24/11 - 2)/2 x 100 = (24/11 - 22/11)/2 x 100 = (2/11)/2 x 100 = 1/11 x 100 = 100/11 percent

We see that choices C, D, E all have 100 in the numerator, so let’s check which of these choices is the correct answer when we substitute k with 20 and m with 10.

C) 100(20 - 10)/(100 + 20) = 100(10)/120 = 100/12

This is not the correct answer.

D) 100(20 - 10)/(100 + 10) = 100(10)/110 = 100/11

This is the correct answer.

Answer: D