Over the last two years, who made more money investing in the stock

Question

Over the last two years, who made more money investing in the stock market, Leslie or Kerri?

(1) Leslie made an average rate of return (arithmetic mean) of 20%, and Kerri made an average rate of return (arithmetic mean) of 5%.
(2) Kerri started with two times as much money as Leslie.

balamoon · Answer

A tough question to explain the solution.

Stmt1 - Though we know Leslie and Kerri's average returns, we have little idea of their total returns. Insufficient.

Stmt 2 - No information of returns. Insufficient.

1+2 - 
Leslie: $100 
Kerri: $200 
Scenario 1 - 
Leslie starts with $100 and makes 20% both years. 
100(1.2)(1.2) = 144 
Kerri starts with $200 and makes %5 both years. 
200(1.05)(1.05) = 220.50 
So  Leslie makes more .
If we prove that Leslie makes less than Kerri's return $20.50, we can conclude   answer E  .

Scenario 2 - 
Leslie makes 80% in the first year and -40%(loss) in the second year (for an average of 80-40/2 = 20% return) 
100(1.8)(.6)= 108 
So  Kerri makes more . 
In this scenario, Leslie did average +20% returns, but she actually gain $8 over the two years.

GMATinsight · Answer

Question : Over the last two years, who made more money investing in the stock market, Leslie or Kerri?

Statement 1 : Leslie made an average rate of return (arithmetic mean) of 20%, and Kerri made an average rate of return (arithmetic mean) of 5%.

Two percentages can NOT be compared unless the relationship of the base values of those percentages is known. Hence,
 NOT SUFFICIENT

Statement 2 : Kerri started with two times as much money as Leslie.
The profit percentage earned by them is unknown. Hence,
 NOT SUFFICIENT

Combining the two Statements  
Let, Starting money with Leslie = $100
Starting money with Kerry = $200

Leslie made 100% profit and 60% loss resulting in average of 20% return per year (Average return =  /2 = 20%)
$100 becomes $200 with 100% profit
$200 becomes $80 with 60% loss
i.e. Loss of $20
Kerry can make consistent 5% profit per year with positive profit 10.25% of 200 = $21
 i.e. Kerry > Leslie

Leslie made 20% profit per year (Average return =  /2 = 20% )
$100 becomes $120 with 20% profit
$120 becomes $144 with 20% profit
i.e. Profit of $44
Kerry can make consistent 5% profit per year with positive profit 10.25% of 200 = $21
 i.e. Kerry < Leslie  
 NOT SUFFICIENT

Answer: Option E

Bunuel · Answer

800score Official Solution:

Though we know Leslie and Kerri's average returns, we have little idea as to what their total returns are.

These abstract questions are best solved with Plug In. This one can be solved by plugging in 1. For example, if Leslie made a 100% rate of return one year and a -60% rate of return the next year, the average rate of return would be (100% – 60%)/2 = 20%.

However, Leslie would only be left with year one 100% and -60% = (1 + 1) (1 – 0.6) = 2(0.4) = 80% of her original investment. This means that she lost 20%!

So statement (1) is insufficient.

Furthermore, statement (2) is clearly insufficient by itself because no returns are given.
Combined with statement (1), statement (2) doesn’t make the distribution of returns any clearer, so  the answer is (E) .

mvictor · Answer

but who would make the average of return %??? this is illogical...makes no sense at all..

GMATinsight · Answer

Hi  mvictor

You don't have to do complete calculation to ensure your answer

Data sufficient Questions don't expect you to solve the question completely they only expect you to think deeps and find the sufficiency of Information to answer the given question

Now Average of 5 may be obtained by taking 10 and 0 on one hand

on the other hand Average of 5 may be obtained by taking 5 and 5

If you can think of such two scenarios then you can do a little calculation to ensure whether the information is sufficient or not

P.S. You don't have to solve the equations to last steps in Data Sufficiency, You only have to figure our the consistency/inconsistensy of solutions obtained

mvictor · Answer

thanks for reply. my point of view was that no person who has knowledge of accounting/finance would do such calculations, as such are illogical at all. this is not how average is calculated for return...

gmat7m · Answer

Pardon my understanding, but isn't the above term too vague. It's averaged out over what? Annual return is just an assumption. What if Leslie started with $100 and made 20% (which is $20) and Kerri started with $400 did the trades several times a day each with a 5% increase. Wouldn't P*1.05*1.05*1.05*......*1.05 be much bigger than P*1.20 in this case?

bumpbot · Answer

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Over the last two years, who made more money investing in the stock

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