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)
https://www.urch.com/forums/gmat-problem-solving
in terms of k and m
This topic has expert replies
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
- 6983manish
- Senior | Next Rank: 100 Posts
- Posts: 65
- Joined: Mon Mar 07, 2011 12:27 am
- Thanked: 6 times
Let initial price of a share is "p"sanju09 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)
https://www.urch.com/forums/gmat-problem-solving
After increase -> p(1 +k/100)
Let initial earning is "e"
After increase -> e(1 +m/100)
percentage rise in price/earning ratio =>
[[{p(1 +k/100)}/{e(1 +m/100)} - (p/e)] / (p/e)]*100
= [(100+k)/100+m) -1]*100
= [100*(k-m)]/(100+m)
Answer D.
- VivianKerr
- GMAT Instructor
- Posts: 1035
- Joined: Fri Dec 17, 2010 11:13 am
- Location: Los Angeles, CA
- Thanked: 474 times
- Followed by:365 members
You could also pick numbers for this one.
If the original price per share of Stock X = 100
Let's say k = 20
New price per share = 120
Original earnings per share of Stock X = 100
Let's say m = 5 (since k > m)
New earnings per share = 105
Old ratio of price/earnings = 100/100 = 1
New ratio of price/earnings = 120/105 = approx 1.14
The percent increase is approx 14%.
Plug in our numbers into the answer choices, and look for the choice that also yields 14%:
A. k/m = 20/5 = 4 too small
B. (k - m) = 20 - 5 = 15 too big
C. 100 (15) / 100 + 20 = 1500 / 120 = 12.5 too small
D. 100 (15) / 100 + 5 = 1500/105 = approx 14. CORRECT!
E. 100 (15) / 100 + 20 + 5 = 1500/125 = 12
If the original price per share of Stock X = 100
Let's say k = 20
New price per share = 120
Original earnings per share of Stock X = 100
Let's say m = 5 (since k > m)
New earnings per share = 105
Old ratio of price/earnings = 100/100 = 1
New ratio of price/earnings = 120/105 = approx 1.14
The percent increase is approx 14%.
Plug in our numbers into the answer choices, and look for the choice that also yields 14%:
A. k/m = 20/5 = 4 too small
B. (k - m) = 20 - 5 = 15 too big
C. 100 (15) / 100 + 20 = 1500 / 120 = 12.5 too small
D. 100 (15) / 100 + 5 = 1500/105 = approx 14. CORRECT!
E. 100 (15) / 100 + 20 + 5 = 1500/125 = 12
Vivian Kerr
GMAT Rockstar, Tutor
https://www.GMATrockstar.com
https://www.yelp.com/biz/gmat-rockstar-los-angeles
Former Kaplan and Grockit instructor, freelance GMAT content creator, now offering affordable, effective, Skype-tutoring for the GMAT at $150/hr. Contact: [email protected]
Thank you for all the "thanks" and "follows"!
GMAT Rockstar, Tutor
https://www.GMATrockstar.com
https://www.yelp.com/biz/gmat-rockstar-los-angeles
Former Kaplan and Grockit instructor, freelance GMAT content creator, now offering affordable, effective, Skype-tutoring for the GMAT at $150/hr. Contact: [email protected]
Thank you for all the "thanks" and "follows"!
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
One approach is to plug in values.sanju09 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 $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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7244
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Let the initial price per share be x and the initial earnings per share be y. After the increase, price per share became x(1 + k/100) and earnings per share became y(1 + m/100). The initial ratio of price per share to earnings per share was x/y and it became [x(1 + k/100)]/[y(1 + m/100)]. Let's apply the percent increase formula:sanju09 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)
Percent increase = 100 * (new - old)/old
Percent increase = 100 * [[x(1 + k/100)]/[y(1 + m/100)] - x/y]/[x/y]
Let's factor out x/y from the numerator and cancel with the denominator:
Percent increase = 100 * [(1 + k/100)/(1 + m/100) - 1]
Percent increase = 100 * [[(100 + k)/100]/[(100 + m)/100]] - 1
Percent increase = 100 * [[(100 + k)/100] * [100/(100 + m)]] - 1
Percent increase = 100 * [(100 + k)/(100 + m) - (100 + m)/(100 + m)]
Percent increase = 100 * [(100 + k - 100 - m)/(100 + m)]
Percent increase = 100 * (k - m)/(100 + m)
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews