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) %
OA is D
Plz. explain this problem
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let
old price = P
old earning = E
new price = P(1+ k /100)
new earnings = E(1+ k /100) Error!!
Edited:
new earnings = E(1+ m /100)
% increase =
[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))
Substitute and solve for ratio
You will easily get D
Let me know if you need more detailed explanation.....
Hope this helps!!
old price = P
old earning = E
new price = P(1+ k /100)
new earnings = E(1+ k /100) Error!!
Edited:
new earnings = E(1+ m /100)
% increase =
[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))
Substitute and solve for ratio
You will easily get D
Let me know if you need more detailed explanation.....
Hope this helps!!
Last edited by stop@800 on Mon Oct 06, 2008 11:08 pm, edited 1 time in total.
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4meonly
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stop@800 wrote:let
old price = P
old earning = E
new price = P(1+ k /100)
new earnings = E(1+ k /100)
% increase =
[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))
Substitute and solve for ratio
You will easily get D
Let me know if you need more detailed explanation.....
Hope this helps!!
Could you please elaborate.
I think I made a mistake somewhere and not able to arrive to correct answer
thanx
You want me to explain which step?
I think may be u want me to explain
new price = P(1+ k /100)
K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100
Please let me know if i missed something.
I think may be u want me to explain
new price = P(1+ k /100)
K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100
Please let me know if i missed something.
-
4meonly
- Legendary Member
- Posts: 891
- Joined: Sat Aug 16, 2008 4:21 am
- Thanked: 27 times
- Followed by:1 members
- GMAT Score:660(
I have some problems with this
[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))
Substitute and solve for ratio
You will easily get D
I think I made some stupid mistake in calculations - can you please post step-by-step calculations?
thanx!
[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))
Substitute and solve for ratio
You will easily get D
I think I made some stupid mistake in calculations - can you please post step-by-step calculations?
thanx!
-
Stockmoose16
- Master | Next Rank: 500 Posts
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Can you explain why my reasoning is wrong?stop@800 wrote:You want me to explain which step?
I think may be u want me to explain
new price = P(1+ k /100)
K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100
Please let me know if i missed something.
I tried to input numbers:
Starting P/E ratio 2:1, ending P/E ratio: 5:2
That means K: 50% and M: 20%... the overall increase in P/E ratio is:
(2.5-2)/2= 25%
None of the answer choices give me 25%....
In addition, I noticed you started changing the numbers into fractions (i.e. k/100), but the question clearly states K%, not K/100%. I don't understand why/how you decided to solve using fractions. Can you explain what's wrong with my example above and also why you went from K% to K/100%?
4meonly wrote:I have some problems with this
[ (new price)/(new earnings) - (old price)/(old earnings) ] / ((old price)/(old earnings))
Substitute and solve for ratio
You will easily get D
I think I made some stupid mistake in calculations - can you please post step-by-step calculations?solving numerator.........
P(1+k/100) / E(1+m/100) - P/E
P(100+k) / E(100+m) - P/E
P/E ( (100+k/100+m) - 1 )
P/E (100+k-100-m)/(100+m)
P/E (k- m)/(100+m)
now we need to divide this by p/e
so we have
(k- m)(100+m)
now adding %
100(k- m)/(100+m) %
PS:
In my earlier post i have written
new earnings = E(1+ k /100)
it shud be
instead new earnings = E(1+ m /100)
thanx!
How you got 50% ??Stockmoose16 wrote:Can you explain why my reasoning is wrong?stop@800 wrote:You want me to explain which step?
I think may be u want me to explain
new price = P(1+ k /100)
K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100
Please let me know if i missed something.
I tried to input numbers:
Starting P/E ratio 2:1, ending P/E ratio: 5:2
That means K: 50% and M: 20%... the overall increase in P/E ratio is:
in increase by K% is increase by a fraction of K/100
(2.5-2)/2= 25%
None of the answer choices give me 25%....
In addition, I noticed you started changing the numbers into fractions (i.e. k/100), but the question clearly states K%, not K/100%. I don't understand why/how you decided to solve using fractions. Can you explain what's wrong with my example above and also why you went from K% to K/100%?
Ex:
increase of 15% is increase by a fraction 15/100 = .15
so for Rs. 200 increase of 15% = increase by 200*.15 = 30
and new value will be 200+30
ie
for P old value
increase is PK/100
and
new value = P + PK/100
Hope this helps!!
-
Stockmoose16
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Sorry, I gave a bad example... now, using the correct numbers, you'll see that my method seems to work. I still don't understand your methodology. Why are you changing things into fractions when the question clearly states: "Stock X increased by K percent." It does not say, "Stock A increased by K/100%." Here's the way I did the problem:stop@800 wrote:How you got 50% ??Stockmoose16 wrote:Can you explain why my reasoning is wrong?stop@800 wrote:You want me to explain which step?
I think may be u want me to explain
new price = P(1+ k /100)
K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100
Please let me know if i missed something.
I tried to input numbers:
Starting P/E ratio 2:1, ending P/E ratio: 5:2
That means K: 50% and M: 20%... the overall increase in P/E ratio is:
in increase by K% is increase by a fraction of K/100
(2.5-2)/2= 25%
None of the answer choices give me 25%....
In addition, I noticed you started changing the numbers into fractions (i.e. k/100), but the question clearly states K%, not K/100%. I don't understand why/how you decided to solve using fractions. Can you explain what's wrong with my example above and also why you went from K% to K/100%?
Ex:
increase of 15% is increase by a fraction 15/100 = .15
so for Rs. 200 increase of 15% = increase by 200*.15 = 30
and new value will be 200+30
ie
for P old value
increase is PK/100
and
new value = P + PK/100
Hope this helps!!
Starting P/E: 50/100
Ending P/E: 75/120
K: (75-50)/50= 50%
M: (120-100)/120=20%
Percent change in p/e is: (5/8-1/2)/1/2 = 1/8/1/2 = 1/4 = 25%
Now, if you plug into answer choice D:
[100 (k-m)] / (100+m) %
you get:
[100 (50-20)] / 100+20) %
(3000/120)
=25%
Is this logic correct? If so, I still don't understand why you put M and K over 100. The question never asks you to create a fraction. It says it's M%, not M/100 %. Please further explain.
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Stockmoose16
- Master | Next Rank: 500 Posts
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- Joined: Mon Aug 04, 2008 1:42 pm
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I tried using your equations and didn't get the correct answer. See the following:stop@800 wrote:How you got 50% ??Stockmoose16 wrote:Can you explain why my reasoning is wrong?stop@800 wrote:You want me to explain which step?
I think may be u want me to explain
new price = P(1+ k /100)
K% increase is actually increase by k/100 fraction
so increase is PK/100
new price = price + increase
P + PK/100
Please let me know if i missed something.
I tried to input numbers:
Starting P/E ratio 2:1, ending P/E ratio: 5:2
That means K: 50% and M: 20%... the overall increase in P/E ratio is:
in increase by K% is increase by a fraction of K/100
(2.5-2)/2= 25%
None of the answer choices give me 25%....
In addition, I noticed you started changing the numbers into fractions (i.e. k/100), but the question clearly states K%, not K/100%. I don't understand why/how you decided to solve using fractions. Can you explain what's wrong with my example above and also why you went from K% to K/100%?
Ex:
increase of 15% is increase by a fraction 15/100 = .15
so for Rs. 200 increase of 15% = increase by 200*.15 = 30
and new value will be 200+30
ie
for P old value
increase is PK/100
and
new value = P + PK/100
Hope this helps!!
(P+PK/100 //E+EM/100) - (P+pm/100 /E +EM/100) // P/E
= P (K-M) / E(100+M) // P/E
= K-m / 100+M
This is not one of the answers. I think something is wrong.
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silentuser
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- Joined: Sun Sep 14, 2008 7:42 pm
Sockmoose16:Stockmoose16 wrote:
I tried using your equations and didn't get the correct answer. See the following:
(P+PK/100 //E+EM/100) - (P+pm/100 /E +EM/100) // P/E
= P (K-M) / E(100+M) // P/E
= K-m / 100+M
This is not one of the answers. I think something is wrong.
Your answer is correct. You just need to multiply it by 100 to get the answer in percentage. Then you will get Choice D.
