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.
_________________

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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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

how are you getting the -m in this step?

\((\frac{100+k}{100+m}-1)*100=(\frac{(100+k-100-m}{100+m})*100\)

\(\frac{100+k}{100+m}-1=\frac{100+k}{100+m}-\frac{100+m}{100+m}=\frac{100+k-100-m}{100+m}\)
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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:
_________________

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

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!

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 ...

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.
_________________

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!

I find it impossible to be solved in <2'

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 ?

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...

hello generis, so what book did you read today ? please tell me in two words

the more i tag you the more new english words i learn from you that will help me during RC and of course working on math

can you please help me to understand this

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

why do we deduct price from percentage or is it increased price denoted as percentage ?

And why are we dividing by fraction \(\frac{x}{y}\), ?? we already have fraction \(\frac{x}{y}\) in numerator ...

have a lovely jovely day / night

Hi dave13 ,

Are you on a mission lately to find demonic
algebra?
I am teasing you. I'm always happy to help if I can.

You wrote: can you please help me to understand this


why do we deduct price from percentage . . .
If you refer to \(\frac{x}{y}\):

1) \(\frac{x}{y} = \frac{P}{E}\) ratio

\(x\) = original price per share
\(y\) = original earnings per share

2) Bunuel is not deducting price from percentage

\(\frac{x}{y}\) is the ORIGINAL or OLD \(\frac{P}{E}\) ratio

He is deducting old \(\frac{P}{E}\) ratio from new \(\frac{P}{E}\) ratio
which must be done
in order to calculate percent change
See below

or is it increased price denoted as percentage ?
Not sure what "it" refers to.
I think it is \(\frac{x}{y}\)

The numerator, \(x\), is indeed
The new price expressed in terms of percent increase (good catch):

\(x\) = original price per share
That price increases by \(k\) percent

\(k\) percent = \(\frac{k}{100}\)

So \(x\) increases by \(k\) percent OF \(x\):
\(x + (\frac{k}{100}*x)\) = new price

Simplify. Factor out the \(x\)
New Price = \(x(1 + \frac{k}{100})\)

Simplify inside the parentheses. \((1 +\frac{k}{100})\)
\(1 = \frac{100}{100}\), so \(\frac{100}{100} + \frac{k}{100} = \frac{100 +k}{100}\)
The \(x\) outside the parentheses is still there. Result: \(\frac{x(100+k)}{100}\)

I can't decide whether you're confused about
subtracting \(\frac{x}{y}\) or \(m\) from \(k\)

Either way, both subtractions happen because . . .
This expression is needed to calculate percent change.

Percent change can be defined as

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

To make the concept of "change" clearer,
percent change can be defined equivalently as

\(\frac{New - Old}{Old} * 100\)

New: \(\frac{x(100+k)}{y(100+m)}\)

Old: \(\frac{x}{y}\)

Try plugging those values into the
second variation of the percent change formula.

And why are we dividing by fraction \(\frac{x}{y}\)? we already have fraction \(\frac{x}{y}\) in numerator ...

We are dividing by \(\frac{x}{y}\) because we are
calculating percent change.

\(\frac{x}{y}\) is . . . the old / original \(\frac{P}{E}\) ratio

See the footnote, which contains an example of fraction to fraction percent change.

This problem is hard.
It contains a strange sort of ratio
(price-per-share to earnings-to-share is
hugely influential but not, IMO, intuitive);
the difference of ratios
(new and old, in which price growth k percent > earnings growth m percent);
AND a percent increase.

You are not a fan
of substituting values, it appears.

If you have not already, please
try going through both of Bunuel's posts
with pencil and paper in hand.
By "both posts" I mean the one you quoted and the one HERE.

I hope that helps.

Example of percent change with a fraction
(please note that I must divide by the original \(\frac{1}{4}\)):

Last year at the zoo, 1 animal in 4 was a newborn
This year at the zoo, 2 animals in 5 were newborns

By what percent did the ratio of newborns to all animals increase?
Percent change:
\((\frac{New - Old}{Old} * 100)\)
\(\frac{\frac{2}{5}-\frac{1}{4}}{\frac{1}{4}}*100\)
\(\frac{\frac{3}{20}}{\frac{1}{4}}*100 = \frac{3}{20}*\frac{4}{1}*100=\)
\(\frac{12}{20}*100=.6 * 100 = 60\) percent increase

P.S. The book I [am] read[ing] today? In two words?
How will you know about this astonishing book? Its title consists of more than two words.
What kind of restriction is THAT?
_________________

Hi
This is one of the basic question and can very well done with in one minute. All you require is practice.Practice a large number of quality questions from gmatclub.



_________________

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.[/quote]


how are you getting the -m in this step?

\((\frac{100+k}{100+m}-1)*100=(\frac{(100+k-100-m}{100+m})*100\)[/quote]


generis, many thanks for taking time to explain i simply would love to improve algebra never was good at it also I like to learn to solve questions in different ways, its not only about GMAT just in life you know

can you please explain in the above mentioned explanation by Bunuel when he reduces by \(\frac{x}{y}\):

before we reduce by \(\frac{x}{y}\) in the numerator there are TWO fractions of \(\frac{x}{y}\): and in the denominator there is ONLY one fraction \(\frac{x}{y}\)

so when we reduce by \(\frac{x}{y}\): BOTH fractions of \(\frac{x}{y}\): dissapear in numerator why ? normally one fraction \(\frac{x}{y}\) should be left after reduction ... by which one ... there is one fraction in fron of brackets and another one with minus sign any idea why this happens /... both fraction in numerator dissapear ?

p.s
books with titles containg more than two words could be some fantasy book
you can tell me two words and i will guess haha like first word and last one:)