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Algebra - Percents

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by sparkles3144 » Tue May 28, 2013 4:28 am
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) %

Original e = e
New earnings = e (1+m/100)

Original p = p
New earnings = p (1+k/100)

I don't know how to proceed from here.

Answer is D

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by mkdureja » Tue May 28, 2013 4:42 am
sparkles3144 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(k - m)] / (100 + k) %
D. [100(k - m)] / (100 + m) %
E. [100(k - m)] / (100 + k + m) %

Original e = e
New earnings = e (1+m/100)

Original p = p
New earnings = p (1+k/100)

I don't know how to proceed from here.

Answer is D

Thanks!
Old ratio: p/e --- A
New ratio: p/e * (100+k)/(100+m) --- B

% change : (B - A)/A * 100
= ((100+k)/(100+m) - 1) * 100
= (100+k-100-m)/(100+m) * 100
= (k-m)/(100+m) * 100
D
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by Brent@GMATPrepNow » Tue May 28, 2013 6:24 am
sparkles3144 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(k - m)] / (100 + k) %
D. [100(k - m)] / (100 + m) %
E. [100(k - m)] / (100 + k + m) %
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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by GMATGuruNY » Tue May 28, 2013 9:13 am
sparkles3144 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(k - m)] / (100 + k) %
D. [100(k - m)] / (100 + m) %
E. [100(k - m)] / (100 + k + m) %
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.
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