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by shahfahad » Thu Nov 26, 2015 9:52 am
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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by Brent@GMATPrepNow » Thu Nov 26, 2015 10:53 am
NOTE: To avoid confusion/ambiguity, I added some brackets.
Q. 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)

Answer: D

Cheers,
Brent
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by Matt@VeritasPrep » Fri Nov 27, 2015 12:09 am
Let's say p = price and e = earnings.

Last year: p/e

This year: ((100 + k)/100)*p / ((100 + m)/100)*e, which is just (100 + k)p / (100 + m)/e

We want the percent increase, so (New - Old)/Old, or

(((100+k)p / (100+m)/e) - (p/e))/(p/e), which is not as bad as it looks in ASCII text, and reduces to

((100 + k)/(100 + m)) - 1, or

((k + 100)-(m + 100))/(100 + m), or

(k - m)/(100 + m)

To convert this to a percent, we then multiply by 100, giving answer D.
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by jawwadali » Tue Oct 25, 2016 11:50 am
Please explain why did we choose "m" as the old value or the denominator ?
Brent@GMATPrepNow wrote:NOTE: To avoid confusion/ambiguity, I added some brackets.
Q. 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)

Answer: D

Cheers,
Brent
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by Brent@GMATPrepNow » Tue Oct 25, 2016 11:56 am
jawwadali wrote:Please explain why did we choose "m" as the old value or the denominator ?
Sorry, I'm not sure which denominator you're referring to.

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Brent
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by fiza gupta » Thu Oct 27, 2016 6:54 am
let price earlier be x
price per share increased by k%
now = x(100+k)/100

let earnings be y
earnings increased by m%
now = y(100+m)/100

price/earnings increase:

[[(x(100+k)/100)/(y(100+m)/100)] - x/y]/x/y * 100
[100+k/100+m] - 1
(100+k-100-m/100+m)*100
=(k-m/100+m)100%
SO D
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by Matt@VeritasPrep » Thu Oct 27, 2016 11:20 pm
jawwadali wrote:Please explain why did we choose "m" as the old value or the denominator ?
We want the ratio of price to earnings, or Price/Earnings. When earnings increase by m%, we're increasing the term in the denominator by m%.
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by Brent@GMATPrepNow » Sat Jan 13, 2018 6:22 am
shahfahad 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: D

Cheers,
Brent
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