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stocks, price per share and earnings

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by Amrabdelnaby » Thu Dec 03, 2015 8:18 am
Dear Pros,

Please help with this.

Last year the price per share of stock X increased by K percent and the earnings 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 & M?

Can someone pls give me a solution using plug ins?

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 %
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by GMATGuruNY » Thu Dec 03, 2015 8:24 am
Check my two posts here:
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by ararjun » Fri Dec 04, 2015 10:29 pm
Amrabdelnaby wrote: Last year the price per share of stock X increased by K percent and the earnings 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 & M?

Can someone pls give me a solution using plug ins?

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 %
Price per share of stock X = P
Earning of each share = E
Old Ratio = P/E

New Price and Earning of each share after increase by K% and M% respectively,
New Price = P*(1+K/100)
New Earnings = E*(1+M/100)
New Ratio = P/E*[(1+K/100)/(1+M/100)]
= P/E*[(100+K)/(100+M)]

Percent increase = (New Ratio - Old Ratio)/Old Ratio
= {P/E*[(100+K)/(100+M)] - P/E}/{P/E}*100%
= {P/E*[(100+K)/(100+M)] - 1}/{P/E}*100%
= {[(100+K)-(100+M)]/(100+M)}*100%
= {K-M)]/(100+M)}*100%

Answer D
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by Brent@GMATPrepNow » Sat Dec 05, 2015 8:28 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 %
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 Brent@GMATPrepNow » Sat Dec 05, 2015 8:29 am
ararjun and I have demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, we have some free videos:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - https://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - https://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
Brent
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