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Q.177, GMAT Review 13th Edition

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by Priyaranjan » Thu Mar 26, 2015 4:59 pm
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 %
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price to earnings ratio

by GMATGuruNY » Thu Mar 26, 2015 5:13 pm
Priyaranjan wrote: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 %
Original ratio:
Let the original price = 1 and the original earnings = 1.
Resulting ratio:
price/earnings = 1/1 = 1.

New ratio:
Let k=200 and m=100.
Since the price increases by k=200%, the new price = 100 + (200/100)(1) = 3.
Since the earnings increase by m=100%, the new earnings = 100 + (100/100)(1) = 2.
Resulting ratio:
(new price)/(new earnings) = 3/2 = 1.5.

Since the old ratio = 1 and the new ratio = 1.5, the ratio increases by 50%. This is our target.
Now plug k=200 and m=100 into the answers to see which yields our target of 50.
Only D works:
100(k-m)/(100+m) = (100)(200-100) / (100+100) = 50.

The correct answer is D.
Last edited by GMATGuruNY on Thu Sep 06, 2018 6:20 am, edited 1 time in total.
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by Brent@GMATPrepNow » Thu Mar 26, 2015 5:19 pm
Priyaranjan wrote: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 %
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
Brent Hanneson - Creator of GMATPrepNow.com
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by Priyaranjan » Thu Mar 26, 2015 7:35 pm
With reference to the response, I've one query. As we've to assume the values of k & m, what if I take k=25 & m=20. If I put forward the values, option (A) is giving a clear result. So, is there any other way to solve the same.

Thanking you
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by GMATGuruNY » Thu Mar 26, 2015 8:12 pm
Priyaranjan wrote:With reference to the response, I've one query. As we've to assume the values of k & m, what if I take k=25 & m=20. If I put forward the values, option (A) is giving a clear result. So, is there any other way to solve the same.

Thanking you
Here is my solution above, using k=25 and m=20:

Original ratio:
Let the original price = 100 and the original earnings = 100.
Resulting ratio:
price/earnings = 100/100 = 1.

New ratio:
Let k=25 and m=20.
Since the price increases by k=25%, the new price = 100 + (25/100)(100) = 125.
Since the earnings increase by m=20%, the new earnings = 100 + (20/100) = 120.
Resulting ratio:
(new price)/(new earnings) = 125/120 = 25/24.

Since the old ratio = 1 = 24/24 and the new ratio = 25/24, the ratio increases by 1/24.
To convert 1/24 to a percentage, multiply by 100:
(1/24) * 100 = 50/12%. This is our target.

Now plug k=25 and m=20 into the answers to see which yields our target of 50/12.
Only D works:
100(k-m)/(100+m) = (100)(25-20) / (100+20) = 500/120 = 50/12.

The correct answer is D.
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by Priyaranjan » Thu Mar 26, 2015 9:02 pm
Sir, thanks for clarifying the same. I think there was a mistake on my part during calculation because of which I got option A as answer instead of D.
GMATGuruNY wrote:
Priyaranjan wrote:With reference to the response, I've one query. As we've to assume the values of k & m, what if I take k=25 & m=20. If I put forward the values, option (A) is giving a clear result. So, is there any other way to solve the same.

Thanking you
Here is my solution above, using k=25 and m=20:

Original ratio:
Let the original price = 100 and the original earnings = 100.
Resulting ratio:
price/earnings = 100/100 = 1.

New ratio:
Let k=25 and m=20.
Since the price increases by k=25%, the new price = 100 + (25/100)(100) = 125.
Since the earnings increase by m=20%, the new earnings = 100 + (20/100) = 120.
Resulting ratio:
(new price)/(new earnings) = 125/120 = 25/24.

Since the old ratio = 1 = 24/24 and the new ratio = 25/24, the ratio increases by 1/24.
To convert 1/24 to a percentage, multiply by 100:
(1/24) * 100 = 50/12%. This is our target.

Now plug k=25 and m=20 into the answers to see which yields our target of 50/12.
Only D works:
100(k-m)/(100+m) = (100)(25-20) / (100+20) = 500/120 = 50/12.

The correct answer is D.
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