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655-705 Level|   Percent and Interest Problems|                              
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vaivish1723
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Last year the price per share of Stock X increased by k percent and 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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D
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Last year the price per share of Stock X increased by k percent and 17 Jan 2010, 13:53
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vaivish1723
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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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):

\(Percent=\frac{Change}{Original}*100\)

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

Answer: D.
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Last year the price per share of Stock X increased by k percent and Updated on: 05 Sep 2023, 02:05
Originally posted by KarishmaB on 15 Jul 2012, 23:44.
Last edited by KarishmaB on 05 Sep 2023, 02:05, edited 2 times in total.
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vaivish1723
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) %
Show more

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

Check out the ratios video here: https://youtu.be/5ODENGG5dvc
and percentages video here: https://youtu.be/HxnsYI1Rws8
and this post on ratios: https://anaprep.com/arithmetic-ratios-t ... ll-starts/
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Last year the price per share of Stock X increased by k percent and 10 Jun 2013, 23:38
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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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Last year the price per share of Stock X increased by k percent and 15 Jul 2012, 06:00
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superpus07
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\(\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}\)

Answer: D.

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

Thanks.
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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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Last year the price per share of Stock X increased by k percent and 15 Jul 2012, 04:06
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Bunuel


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

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

Thanks.
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Last year the price per share of Stock X increased by k percent and 06 May 2013, 06:53
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vaivish1723
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) %
Show more

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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Last year the price per share of Stock X increased by k percent and Updated on: 08 Nov 2015, 23:49
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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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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Last year the price per share of Stock X increased by k percent and 10 Jan 2015, 07:32
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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%

Hence, Answer: D
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Last year the price per share of Stock X increased by k percent and 03 Jan 2016, 11:25
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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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Last year the price per share of Stock X increased by k percent and 13 Mar 2016, 08:11
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VeritasPrepKarishma
vaivish1723
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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Karishma, in what cases would you advise to put in values rather than solve algebraically?
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Last year the price per share of Stock X increased by k percent and 13 Mar 2016, 21:21
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vaivish1723
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) %
Show more

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 14 Mar 2016, 01:19
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vaivish1723
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?
Show more

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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Last year the price per share of Stock X increased by k percent and 19 Jun 2016, 18:33
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vaivish1723
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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How did you go from 12/11 to an increase of 100/11 percent?
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Last year the price per share of Stock X increased by k percent and 19 Jun 2016, 21:24
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vaivish1723
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

How did you go from 12/11 to an increase of 100/11 percent?
Show more

According to original prices, PPS/EPS = 1
After the increase, PPS/EPS = 12/11

Percentage Increase in PPS/EPS \(=\frac{ (\frac{12}{11} - 1)}{1} * 100 = \frac{100}{11} %\)
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Last year the price per share of Stock X increased by k percent and 08 Jul 2016, 08:59
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Bunuel
superpus07
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\(\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}\)

Answer: D.

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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how are you getting the -m in this step?

\((\frac{100+k}{100+m}-1)*100=(\frac{(100+k-100-m}{100+m})*100\)
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how are you getting the -m in this step?

\((\frac{100+k}{100+m}-1)*100=(\frac{(100+k-100-m}{100+m})*100\)
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\(\frac{100+k}{100+m}-1=\frac{100+k}{100+m}-\frac{100+m}{100+m}=\frac{100+k-100-m}{100+m}\)
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Last year the price per share of Stock X increased by k percent and Updated on: 19 Jan 2020, 13:49
Originally posted by BrentGMATPrepNow on 26 Jul 2016, 11:21.
Last edited by BrentGMATPrepNow on 19 Jan 2020, 13:49, edited 2 times in total.
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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. 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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Let's use the INPUT-OUTPUT approach.

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:
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Last year the price per share of Stock X increased by k percent and Updated on: 19 Jan 2020, 13:49
Originally posted by BrentGMATPrepNow on 15 Oct 2016, 09:37.
Last edited by BrentGMATPrepNow on 19 Jan 2020, 13:49, edited 1 time in total.
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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) k/m %
(B) (k–m) %
(C) 100(k-m)/100+k %
(D) 100(k-m)/100+m %
(E) 100(k-m)/100+k+m %
Show more

One 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:
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Last year the price per share of Stock X increased by k percent and 09 Sep 2017, 21:51
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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. 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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hi

Would you please speak few more words about the expression "((100+k)/(100+m) - 1)" ....? especially about 1...? Is this something as such that "1", when subtracted from a fraction reveals the change, increase or decrease ....?

thanks in advance ...
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