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

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Re: Last year the price per share of Stock X increased by k percent and [#permalink]

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19 Jun 2016, 20:24
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

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

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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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 12 Apr 2014 Posts: 9 Re: Last year the price per share of Stock X increased by k percent and [#permalink] ### Show Tags 19 Jun 2016, 23:08 to keep it simple for solving....assume EPS and PPS to be 100...covert quant lang to maths....((more-less)*100)less to get the answer in terms of K and M Manager Joined: 22 Sep 2015 Posts: 110 Re: Last year the price per share of Stock X increased by k percent and [#permalink] ### Show Tags 08 Jul 2016, 07:59 1 This post received KUDOS Bunuel wrote: superpus07 wrote: Bunuel wrote: $$\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}$$ 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. how are you getting the -m in this step? $$(\frac{100+k}{100+m}-1)*100=(\frac{(100+k-100-m}{100+m})*100$$ Math Expert Joined: 02 Sep 2009 Posts: 43851 Re: Last year the price per share of Stock X increased by k percent and [#permalink] ### Show Tags 08 Jul 2016, 08:16 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED nycgirl212 wrote: how are you getting the -m in this step? $$(\frac{100+k}{100+m}-1)*100=(\frac{(100+k-100-m}{100+m})*100$$ $$\frac{100+k}{100+m}-1=\frac{100+k}{100+m}-\frac{100+m}{100+m}=\frac{100+k-100-m}{100+m}$$ _________________ SVP Joined: 11 Sep 2015 Posts: 2055 Location: Canada Last year the price per share of Stock X increased by k percent and [#permalink] ### Show Tags 26 Jul 2016, 10:21 Expert's post Top Contributor 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'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: [Reveal] Spoiler: D RELATED VIDEOS _________________ Brent Hanneson – Founder of gmatprepnow.com Last edited by GMATPrepNow on 13 Jan 2018, 06:22, edited 1 time in total. SVP Joined: 11 Sep 2015 Posts: 2055 Location: Canada Re: Last year the price per share of Stock X increased by k percent and [#permalink] ### Show Tags 15 Oct 2016, 08:37 Expert's post Top Contributor SW4 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 % 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)

[Reveal] Spoiler:
D

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

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12 May 2017, 16:56
I solved it as below:

Old Price = x, Old Earnings = y, Old Ratio = x/y

New Price = x + k% x = x (1+k/100) = x ( k + 100)/100
New Earnings = y + m% y = y ( 1+m/100) = y ( m+100)/100

New Ration = x(k+100) / y(m+100)
We need to find New Ratio is how much % greater than old ratio. This is the key point to understand and represent.

Expressing in Mathematical Form:
New Ratio = p% more than Old Ratio
New Ratio = Old Ratio + p% Old Ratio
x(100+k)/y(100+m) = x/y ( 1 + p/100)
Simplifying
p = (k-m)*100/m+100.
Option D
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Re: Last year the price per share of Stock X increased by k percent and [#permalink]

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04 Jul 2017, 11:31
Because this percent question doesn't ask for the actual numbers anywhere, we can plug in numbers

Let us say the original price = 100, and the original earnings = 200 (I chose different numbers just to make sure they didn't accidentally cancel each other out somewhere)

Word problems are hard for me, and especially when it's asking for multiple things things like this one (a ratio, a difference of ratios, and a percent) so I wrote down in a formula what the last sentence was asking for:

The percent increase of the two ratios = 100* [(ratio 2 - ratio 1)/(ratio 1)

Ratio 1 = original price/original earnings = 100/200 = 1/2

Ratio 2 = new price/new earnings
new price = 100*(1+(k/100) = 100 + (100k/100) = 100 + k
New earning = 200*(1+m/100) = 200 + 200m/100 = 2(100+m
Ratio 2 = (100+k)/2(100+m)

Solve for the percent inscrease of the two ratios
((100+k)/2(100+m)) - 1/2)/1/2
((100+k)/2(100+m) - (100 + m)/2(100+m))/12
(100+k-100-m)/2(100+m) / (1/2)
(k-m)/2(100+m) * 2
(k-m)/(100+m) * 100 (we multiply by 100 to get it in % form)
100(k-m)/(100+m)
D!
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Re: Last year the price per share of Stock X increased by k percent and [#permalink]

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09 Sep 2017, 20:51
SravnaTestPrep 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) %

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)

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 ....?

Director
Joined: 17 Dec 2012
Posts: 627
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Re: Last year the price per share of Stock X increased by k percent and [#permalink]

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09 Sep 2017, 21:03
gmatcracker2017 wrote:
SravnaTestPrep 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) %

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)

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 ....?

Hi,

Percent increase =( (New value - original value)/ original value ) * 100
New value = (100+k)/(100+m)

Original value=1

Substituting the above values you get the answer.
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Sravna
http://www.sravnatestprep.com

Standardized Approaches

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

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01 Dec 2017, 13:27
Experts,

Could you kindly suggest other similar problems to practice on?

Aside from the link below that is:
https://gmatclub.com/forum/currently-y- ... l#p1318632

Thanks a lot!
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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 Dec 2017, 00:36
I find it impossible to be solved in <2'
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Re: Last year the price per share of Stock X increased by k percent and [#permalink]

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19 Dec 2017, 00:33
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. $$\frac{k}{m} %$$

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):

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

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

Hi Bunuel,

Why cant we use the following formula to get the answer:

numerator: the delta increase, calculated as follows:

x . k% divided by y . m% -> this will give us the delta increase of the ratio

denominator: x divided by y (the original ratio)

both numerator and denominator then multipled by 100 to get the percent. I did this calculation and got 100k/m% as a result - did i miss anything ?
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Re: Last year the price per share of Stock X increased by k percent and [#permalink]

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26 Dec 2017, 23:46
Fernandocma wrote:
I find it impossible to be solved in <2'

I agree, it is time consuming one... Substitution would work if you pick up convenient numbers like 100/100 and increase by 200 and 100, otherwise, substitution is time consuming...
Re: Last year the price per share of Stock X increased by k percent and   [#permalink] 26 Dec 2017, 23:46

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