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# Last year the price per share of Stock X increased by k percent and

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

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17 Jan 2010, 11:10
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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. $$\frac{k}{m} %$$

B. $$(k – m) %$$

C. $$\frac{100(k – m)}{(100 + k)} %$$

D. $$\frac{100(k – m)}{(100 + m)} %$$

E. $$\frac{100(k – m)}{(100 + k + m)} %$$
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Last year the price per share of Stock X increased by k percent and  [#permalink]

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17 Jan 2010, 13:53
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vaivish1723 wrote:
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. $$\frac{k}{m} %$$

B. $$(k – m) %$$

C. $$\frac{100(k – m)}{(100 + k)} %$$

D. $$\frac{100(k – m)}{(100 + m)} %$$

E. $$\frac{100(k – m)}{(100 + k + m)} %$$

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):

$$Percent=\frac{Change}{Original}*100$$

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}$$

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10 Jun 2013, 23:38
21
6
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.

Hope this help many.
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##### General Discussion
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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15 Jul 2012, 04:06
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Bunuel wrote:

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}$$

Could you explain step-wise how you derived his one? I keep missing one step.

Thanks.
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Posts: 59588
Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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15 Jul 2012, 06:00
27
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superpus07 wrote:
Bunuel wrote:

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}$$

Could you explain step-wise how you derived his one? I keep missing one step.

Thanks.

Sure: $$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100$$ --> reduce by $$\frac{x}{y}$$:

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{\frac{100+k}{100+m}-1}{1}100=(\frac{100+k}{100+m}-1)*100=(\frac{100+k-100-m}{100+m})*100=\frac{100(k-m)}{100+m}$$.

Hope it's clear.
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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15 Jul 2012, 23:44
76
22
vaivish1723 wrote:
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) %

Put in some values to figure it out.

Say original Price per share (PPS) = $100 and original Earnings per share (EPS) =$100
Ratio PPS/EPS = 100/100 = 1

Say PPS increased by 20% (k) and became 120
Say EPS increased by 10% (m) and became 110
Ratio PPS/EPS = 12/11

This is an increase of 1/11 = 100/11 %

Only option (D) gives you 100/11 when k = 20 and m = 10
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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29 Mar 2013, 10:26
Bunuel wrote:
superpus07 wrote:
Bunuel wrote:

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}$$

Could you explain step-wise how you derived his one? I keep missing one step.

Thanks.

Sure: $$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100$$ --> reduce by $$\frac{x}{y}$$:

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{\frac{100+k}{100+m}-1}{1}100=(\frac{100+k}{100+m}-1)*100=(\frac{100+k-100-m}{100+m})*100=\frac{100(k-m)}{100+m}$$.

Hope it's clear.

Hi could you explain please why do you convert x/y into 1?
thanks
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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29 Mar 2013, 11:18
1
1
Bunuel wrote:
superpus07 wrote:
Bunuel wrote:

Could you explain step-wise how you derived his one? I keep missing one step.

Thanks.

Sure: $$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100$$ --> reduce by $$\frac{x}{y}$$:

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{\frac{100+k}{100+m}-1}{1}100=(\frac{100+k}{100+m}-1)*100=(\frac{100+k-100-m}{100+m})*100=\frac{100(k-m)}{100+m}$$.

Hope it's clear.

Hi could you explain please why do you convert x/y into 1?
thanks

$$\frac{\frac{x}{y}}{\frac{x}{y}} = \frac{x}{y} * \frac{y}{x}=1$$
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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06 May 2013, 06:53
6
4
vaivish1723 wrote:
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) %

Responding to a pm: (super detailed steps)
When you have variables in the question and variables in the options, one method of getting to the answer is by assuming values for the variables. If a question says: x is greater than y/3 but less than y/2. Which of the following relations must hold?
(A) y < x < 2y
(B) 2y < 6x < 3y
...
...

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 < x < 2y -----> 60 < 25 < 2*120 ( does not hold)
(B) 2y < 6x < 3y ------> 2*60 < 6*25 < 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.

We can do this question using the same concept.
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 = 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 = 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)% = 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)
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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25 Jan 2014, 13:52
1
but this number plugin should only work when you assume that price = earnings ?

VeritasPrepKarishma wrote:
vaivish1723 wrote:
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) %

Put in some values to figure it out.

Say original Price per share (PPS) = $100 and original Earnings per share (EPS) =$100
Ratio PPS/EPS = 100/100 = 1

Say PPS increased by 20% (k) and became 120
Say EPS increased by 10% (m) and became 110
Ratio PPS/EPS = 12/11

This is an increase of 1/11 = 100/11 %

Only option (D) gives you 100/11 when k = 20 and m = 10
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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16 Jul 2014, 05:24
Bunuel wrote:
vaivish1723 wrote:
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) %

OA

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):

$$Percent=\frac{Change}{Original}*100$$

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}$$

HI Bunuel,

Similar kind of question is mentioed on following link

currently-y-percent-of-the-members-on-the-finance-committee-33127.html

I just want to know what is the best way. I tried the above question is doable without picking numbers. but the question mentioned on above link i stuck there. Please provide your comments on the question mentioed in above link.

Thanks
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Posts: 59588
Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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17 Jul 2014, 10:05
PathFinder007 wrote:
Bunuel wrote:
vaivish1723 wrote:
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) %

OA

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):

$$Percent=\frac{Change}{Original}*100$$

$$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}$$

HI Bunuel,

Similar kind of question is mentioed on following link

currently-y-percent-of-the-members-on-the-finance-committee-33127.html

I just want to know what is the best way. I tried the above question is doable without picking numbers. but the question mentioned on above link i stuck there. Please provide your comments on the question mentioed in above link.

Thanks

Number plugging approach is in Karishma's post there: currently-y-percent-of-the-members-on-the-finance-committee-33127.html#p1318632
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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Updated on: 08 Nov 2015, 23:49
3
1
I think this type of problems lends itself well to easy number picking:

(P) share price= 100
(E) earnings=100
P/E = 1

Let k=200 and m=50

New P/E = 100*{(100+200)/100} / 100*{(100+50)/100} = 2 so increase of 100%

1) 200/50= 4 % wrong
2) 200-50= 150% wrong
3) 100(200-50)/(100+200)= (100*150)/300=50% wrong
4) 100(200-50)/(100+50)= (100*150)/150 = 100% Right
5) 100(200-50)/(100+200+50)= 100*150/350= wrong

--> Ans D
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Originally posted by NoHalfMeasures on 29 Jul 2014, 08:03.
Last edited by NoHalfMeasures on 08 Nov 2015, 23:49, edited 2 times in total.
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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10 Jan 2015, 07:32
1
4
Earlier year share price = P
Earlier earnings = E
Ratio = P/E

Assume:
k = 50%
m = 25%

Therefore:
New share price = 1.5P
New earnings = 1.25E
New Ratio: 1.5P/1.25E = 150P/125E = 6P/5E = [1 + (1/5)]P/E
i.e. P/E ratio increased by 1/5 or 20%

Now, plug k = 50 and m = 25 in solutions. Only D yields 20%

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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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03 Jan 2016, 11:25
2
First year:

Price = P
Earnings = E
Ratio#1 = P/E

Second year:

Price = P*K/100 + P
Earnings = E*M/100 + E
Ratio#2 = (P*K/100 + P)/(E*M/100 + E)

Percent increase in ratio = ((ratio#2 - ratio#1)/(ratio#1))*100
Percent increase in ratio = (((P*K/100 + P)/(E*M/100 + E) - P/E)/(P/E))*100

= ((K/100 + 1)/(M/100 + 1) - 1)*100

(K/100 + 1 - M/100 - 1)/(M/100 + 1)

=((K - M)/(M + 100))100
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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13 Mar 2016, 08:11
VeritasPrepKarishma wrote:
vaivish1723 wrote:
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) %

Put in some values to figure it out.

Say original Price per share (PPS) = $100 and original Earnings per share (EPS) =$100
Ratio PPS/EPS = 100/100 = 1

Say PPS increased by 20% (k) and became 120
Say EPS increased by 10% (m) and became 110
Ratio PPS/EPS = 12/11

This is an increase of 1/11 = 100/11 %

Only option (D) gives you 100/11 when k = 20 and m = 10

Karishma, in what cases would you advise to put in values rather than solve algebraically?
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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13 Mar 2016, 20:53
i tried to use values..
suppose k=80, and m=50
then we have 20% increase of the ratio.
if we plug in the values, then only D works.
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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13 Mar 2016, 21:21
7
vaivish1723 wrote:
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) %

Let Original price =100
Let original earnings per share =100
Price/ earnings =1

New price = 100+k
New earnings per share= 100+m
price /earnings = (100+k)/(100+m)

Percent increase =((100+k)/(100+m) - 1) *100
= (k-m)*100/(100+m)
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Last year the price per share of Stock X increased by k percent and  [#permalink]

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Updated on: 22 Dec 2017, 22:04
vaivish1723 wrote:
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) %

I just plugged in values for k = 20 and m = 10.
The answer you get is 100/11
Again, I plugged in values for k and m in the options.
Only option D is true.
Alternatively.
Let price per share is 100 and earnings per share is 100; the ratio is 1.
After increase, the ratio is (100+k)/(100+m).
The difference between these two ratios is (k-m)/(100+m)
Therefore, the required percentage is 100(k-m)/(100+m)

Originally posted by Mathivanan Palraj on 13 Mar 2016, 21:37.
Last edited by Mathivanan Palraj on 22 Dec 2017, 22:04, edited 1 time in total.
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Re: Last year the price per share of Stock X increased by k percent and  [#permalink]

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14 Mar 2016, 01:19
Viktoriaa wrote:
VeritasPrepKarishma wrote:
vaivish1723 wrote:
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) %

Put in some values to figure it out.

Say original Price per share (PPS) = $100 and original Earnings per share (EPS) =$100
Ratio PPS/EPS = 100/100 = 1

Say PPS increased by 20% (k) and became 120
Say EPS increased by 10% (m) and became 110
Ratio PPS/EPS = 12/11

This is an increase of 1/11 = 100/11 %

Only option (D) gives you 100/11 when k = 20 and m = 10

Karishma, in what cases would you advise to put in values rather than solve algebraically?

When the question doesn't give any concrete numbers and talks in terms of variables (the answer options would also be in terms of variables in that case), you can plug in values to get to the answer.
Percentage questions often provide an opportunity to plug in values too, say 100 for a base value.
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Re: Last year the price per share of Stock X increased by k percent and   [#permalink] 14 Mar 2016, 01:19

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