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

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25 Mar 2009, 23:06

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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) %

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

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?

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):

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
_________________

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.

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.

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