Problem Solving

Hi tapanmittal,

When posting questions, you should include the 5 answer choices. In many prompts, the answers provide 'clues' as to how you might choose to approach the prompt. Since most GMAT questions can be approached in a variety of ways, knowing more than just the 'math approach' will help you to attack prompts in the fastest/easiest fashion and avoid the types of pacing issues that impact many Test Takers.

GMAT assassins aren't born, they're made,
Rich

tapanmittal wrote:Last year the price per share of stock X increased by k% and the earnings per share of stock X increased by m%,where>m.
By what percent did the ratio of price per share to earnings per share increase,in terms of k and m?

Ans-100(k-m)%/100+m

Searching for a shortest solution to approach such problems.

177) 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) %

Solution:

To start, we need to define a few variables.

p = price per share of stock X

e = earnings per share of stock X

We are given that the price per share of stock X increased by k percent. We can express this as:

p(1 + k/100) = p((100 + k)/100)

We are also given that the earnings per share of stock X increased by m percent. We can express this as:

e(1 + m/100) = e((100 + m)/100)

Finally, we are asked by what percent the ratio of the price per share to earnings per share increased. We'll set up our two ratios and then plug those into the percent change formula. While the math that is produced here may seem a bit complicated, it is not too bad as long as we take our time and stay focused.



Answer:D

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