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# Last year the price per share of Stock X increased by k perc

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Last year the price per share of Stock X increased by k perc [#permalink]  25 Mar 2009, 22:06
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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) %

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-the-price-per-share-of-stock-x-increased-by-k-89307.html
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Re: Percentage [#permalink]  26 Mar 2009, 12:45
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milind1979 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) %
6
C. [100(k – m)] / (100 + k) %
D. [100(k – m)] / (100 + m) %
E. [100(k – m)] / (100 + k + m) %

Price Per Share (PPS) = x
Earning Per Share(EPS) = y

Increased PPS = x(1+k/100)
Increased EPS = y(1+m/100)

% increase in the ratios (PPS/EPS) = {[x(100+k)]/[y(100+m)] - (x/y)} / (x/y)

On Simplifying, % increase = [100(k-m)] / (100 + m) % , hence (D).
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Re: Percentage [#permalink]  19 Dec 2010, 15:39
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I still don't understand how you got from the percent increase equation to the final selection of D? What steps were taken to arrive at the simplified D expression?
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Re: Percentage [#permalink]  19 Dec 2010, 15:49
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gettinit wrote:
I still don't understand how you got from the percent increase equation to the final selection of D? What steps were taken to arrive at the simplified D expression?

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 price - $$x$$
Original earnings - $$y$$
Original ratio price per earnings - $$\frac{x}{y}$$

Increased price - $$x(1+\frac{k}{100})=\frac{x(100+k)}{100}$$
Increased earnings - $$y(1+\frac{m}{100})=\frac{y(100+m)}{100}$$
New ratio price per earnings - $$\frac{x(100+k)}{y(100+m)}$$

General formula for percent increase or decrease, (percent change):

$$Percent=\frac{Change}{Original}*100$$

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=(\frac{100+k}{100+m}-1)100=\frac{100(k-m)}{100+m}$$

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Re: Percentage [#permalink]  23 Dec 2010, 17:52
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Ahh thanks Bunuel that clears things up. It was the multiplication with a 100 I was leaving off.
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Re: Percentage [#permalink]  23 Dec 2010, 18:26
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It should be D. Tricky one.
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Re: Percentage [#permalink]  23 Dec 2010, 21:57
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@ bunuel

I am good at calculating % and hardly face any difficulty with % probs or any other time,rate, distance probs

But, whenever i see the probs asked in terms of alphabetical notions instead of actual nos, i take a lot of time and make lot many mistakes. what is the best approach in addressing such probs e.g. if this same problem had real nos instead of k,m etc, i could easily solve it , but this alpha notations made me take some 3 to 4 mins for this prob
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Re: Percentage [#permalink]  10 Jun 2013, 22:12
hirendhanak wrote:
@ bunuel

I am good at calculating % and hardly face any difficulty with % probs or any other time,rate, distance probs

But, whenever i see the probs asked in terms of alphabetical notions instead of actual nos, i take a lot of time and make lot many mistakes. what is the best approach in addressing such probs e.g. if this same problem had real nos instead of k,m etc, i could easily solve it , but this alpha notations made me take some 3 to 4 mins for this prob

Bunuel, I'm in the same boat, albeit three years late. Would be great if you (or someone else) could address the above question.
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Re: Percentage [#permalink]  10 Jun 2013, 22:38
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The best way to solve such questions is to use Numbers. Let me show, how it works-
Pick Numbers which are easy to work with.
Lets assume that the Price of share before increase = 100
Assume k= 50%
So the price of share after increase = 150

Lets assume that the EPS before increase = 100
Assume m= 20%
So the EPS after increase = 120

Ratio of Price/EPS before increase = 100/100= 1
Ratio of Price/EPS after increase = 150/120= 1.25 ( a 25% percent increase, which we want to calculate & is obscured in terms of k & m)

To find the correct option, plug the value of k & m in options
A. k m % = 50 x 20 = 1000 = No
B. (k – m) % = 50-20 = 30 = No
C. [100(k – m)] / (100 + k) % = 100 (50-20)/(100+50) = 3000/150 = 20 -No
D. [100(k – m)] / (100 + m) % = 100 (50-20)/(100+20) = 3000/120 = 25 -Bingo
E. [100(k – m)] / (100 + k + m) % - Don't need to check this one.

Hope this help many.
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Re: Percentage   [#permalink] 10 Jun 2013, 22:38
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