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?	Options:	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) %
One way of doing this is assuming some value for y. Say, y = 60. So x is greater than 20 but less than 30. Say x could be 25.   Not put y = 60 and x = 25 in the options:   (A) y &lt; x &lt; 2y -----&gt; 60 &lt; 25 &lt; 2*120 ( does not hold)   (B) 2y &lt; 6x &lt; 3y ------&gt; 2*60 &lt; 6*25 &lt; 3*60 (holds so could be the answer)   Mind you, you need to check every option to ensure that the relation holds for only one option. If it holds for more than one options, you will need to check for some other values too.   The point is that we assume values and then plug them in the options to see which relation works.   Last Year:   Price per share (PPS) increased by k%. Let's say k = 20. So if the price was 100, it increased by 20% to become 120 (New PPS).   Earnings per share increased by m%. Let's say m = 10 (m must be less than k). So if earnings per share was also 100, it increased by 10% to become 110 (New EPS).   By what percent did the ratio of price per share to earnings per share increase?   Ratio of PPS/EPS was   100/100= 
<gadget id="calculator">  100/100</gadget>
<output>1</output>
1   New ratio= New PPS/ New EPS = 120/110 = 1.0909   %Increase = [(1.0909 - 1)/1] * 100 = 9.09%   Now, in the options, put k (1.0909 - 1)/1  * 100= 
<gadget id="calculator">(1.0909 - 1)/1  * 100</gadget>
<output>9.09</output>
9.09%   Now, in the options, put k= 20, m = 10   Only (D) will give you 9.09%. Let me show you calculations of some of the options.   B. (k – m) %     (20 - 10)= 
<gadget id="calculator">  (20 - 10)</gadget>
<output>10</output>
10% (Not the answer)   C. [100(k – m)] / (100 + k) %   [100(20 - 10)]/(100 + 20) %= 1000/120 % = 8.3% (Not the answer)   D. [100(k – m)] / (100 + m) %   [100(20 – 10)] / (100 + 10) % = 1000/11 % = 9.09% (Answer) answer is [100(k – m)] / (100 + m) %
<result>D</result>
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?