Math Q from Sets

[rajkoneru]

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) %

How do you solve this?

[Nov1907]

p-price per share. e-earnings per share. New price per share = p(1+k/100). New Earnings per share = e(1+m/100).

Original ratio of Price per share to Eanings per share = p/e
New Ratio of Price per share to Eanings per share = [p(1+k/100)]/[e(1+m/100)] = p(100+k)/e(100+m)

% inc. = 100*{[p(100+k)/e(100+m) -p/e]/(p/e)} (since it says k is greater than m the new value must be higher.)
= 100*(k-m)/(100+m).

Ans. D

[tricia.lin]

Question, is there a way to solve this using smart numbers?

[RonPurewal]

re: "smart numbers" -- absolutely!

in fact, when you see a problem that looks like this (with a huge load of variables spilled all over the floor), you may as well automatically consider the pick-your-own-numbers approach.

let's say that the price and earnings were both 1. now let's say the price increases to 3 (a gain of 200%, so k = 200), and the earnings increase to 2 (a gain of 100%, so m = 100).

* the old ratio of p/e was 1/1 = 1.

* the new p/e ratio is 3/2 = 1.5.

so, the desired answer is the percent increase from 1 to 1.5, which is 50%.

check the choices:
(a) 200/100 = 2%. nope
(b) 200 - 100 = 50%. no sir
(c) 100(100)/300 = 33.333....%. no way josé
(d) 100(100)/200 = 50%. sweetness.
(e) 100(100)/400 = 25%. uh-uh

... so it's (d).

you may have to try a couple of different sets of values to get a non-icky value for the final answer. but, if you just keep plowing, you'll get it.