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 Post subject: GMAT Percentage (Data Sufficiency)
PostPosted: Mon Nov 01, 2010 5:50 pm 
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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.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(E) 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).
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Isn't C the correct answer option? Using 1 and 2 together, if we assume Leslie invested x dollars then Kerri invested 2x dollars. Now using the average returns, Leslie made 1.2x (20% return on x dollars) dollars whereas Kerri made 2.1x dollars (5% return on 2x dollars). Thus, clearly Kerri made more money than Leslie.


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 Post subject: Re: math (test 2, question 28): percentages, data sufficienc
PostPosted: Mon Nov 01, 2010 6:31 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
The following passage in you reasoning is NOT true:
"Now using the average returns, Leslie made 1.2x (20% return on x dollars) dollars whereas Kerri made 2.1x dollars (5% return on 2x dollars)."

You may read the first three paragraphs in the explanation, or try a new one:

The question statement implies that if Leslie had invested x dollars then she had x × (1 + n/100) dollars at the end of the first year and x × (1 + n/100) × (1 + m/100) dollars at the end of the second year.
n% is the first-year return
m% is the second-year return
Therefore the statement (1) tells us that (n + m)/2 = 20.

The question statement implies that if Leslie had invested x dollars then Kerri had invested 2x dollars. Kerrie had 2x × (1 + a/100) dollars at the end of the first year and 2x × (1 + a/100) × (1 + b/100) dollars at the end of the second year.
a% is the first-year return
b% is the second-year return
Therefore the statement (1) tells us that (a + b)/2 = 5.

If x = 100, m = n = 20 and a = 10, b = 0 then:
Leslie made 100 × (1 + 0.2) × (1 + 0.2) – 100 = 144 – 100 = 44 dollars.
Kerri made 200 × (1 + 0.1) × (1 + 0) – 200 = 220 – 200 = 20 dollars.
Therefore Leslie made more than Kerri in this case.
PROFIT/LOSS diagram:
Image

If x = 100, n = 80, m = -40 and a = 10, b = 0 then:
Leslie made 100 × (1 + 0.8) × (1 – 0.4) – 100 = 108 – 100 = 8 dollars.
Kerri made 200 × (1 + 0.1) × (1 + 0) – 200 = 220 – 200 = 20 dollars.
Therefore Leslie made less than Kerri in this case.
PROFIT/LOSS diagram:
Image

So the both statements taken together are NOT sufficient to answer the question.


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