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Zorluk: OrtaData Sufficiency with Visual and Tabular Contexts

An investment portfolio consists of three funds: Fund Alpha, Fund Beta, and Fund Gamma. The table below presents the capital committed (in millions of dollars) and the annual yield percentage for each fund during the past fiscal year:

FundCapital Committed ($ millions)Annual Yield (%)
Fund Alpha408%
Fund Beta6012%
Fund Gammaccy%y\%

What was the overall annual yield percentage for the combined portfolio of all three funds?

(1) The capital committed to Fund Gamma, cc, was equal to the total capital committed to Fund Alpha and Fund Beta combined.
(2) The annual yield percentage for Fund Gamma, y%y\%, was equal to the weighted average annual yield percentage of Fund Alpha and Fund Beta combined.

  1. A
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.Cevap
  3. C
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. D
    EACH statement ALONE is sufficient.
  5. E
    Statements (1) and (2) TOGETHER are NOT sufficient.

Cevap

Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient.
The option stating that Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient is correct. Fund Alpha and Fund Beta combined have a weighted average yield of 40(8%)+60(12%)100=10.4%\frac{40(8\%) + 60(12\%)}{100} = 10.4\%. Statement (2) tells us that Fund Gamma's yield is also 10.4%10.4\%. Combining any two groups with identical average yields results in an overall average yield equal to 10.4%10.4\%, regardless of the amount of capital cc in Fund Gamma. Statement (1) provides only the capital amount c=100c = 100, leaving the yield yy unknown and thus insufficient.

Adım Adım Çözüm

1
Formulate the algebraic expression for the overall portfolio yield.
Overall Portfolio Yield = 40(8%)+60(12%)+c(y%)40+60+c=3.2+7.2+cy100100+c=10.4+cy100100+c\frac{40(8\%) + 60(12\%) + c(y\%)}{40 + 60 + c} = \frac{3.2 + 7.2 + \frac{cy}{100}}{100 + c} = \frac{10.4 + \frac{cy}{100}}{100 + c}
The total annual return is the sum of returns from each fund, divided by total capital committed.
2
Calculate the combined weighted average yield of Fund Alpha and Fund Beta.
Sub-portfolio yield = 40(8)+60(12)40+60=320+720100=10.4%\frac{40(8) + 60(12)}{40 + 60} = \frac{320 + 720}{100} = 10.4\%
Determining the performance of the known portion of the portfolio simplifies statement evaluation.
3
Evaluate Statement (1) independently: c=40+60=100c = 40 + 60 = 100.
Overall Yield = 10.4+y200×100%=10.4+y2%\frac{10.4 + y}{200} \times 100\% = \frac{10.4 + y}{2}\%. Since yy is unknown, this value is not unique.
Without knowing Fund Gamma's yield rate y%y\%, the capital amount alone does not provide a definitive overall yield.
4
Evaluate Statement (2) independently: y%=10.4%y\% = 10.4\%.
Overall Yield = 100(10.4%)+c(10.4%)100+c=10.4%(100+c)100+c=10.4%\frac{100(10.4\%) + c(10.4\%)}{100 + c} = \frac{10.4\%(100 + c)}{100 + c} = 10.4\%.
When a new component is added to a group with a value equal to the group's current average, the overall average remains unchanged regardless of the size (cc) of the new component.

Anahtar Kavram

Weighted Average Invariance in Data Sufficiency
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Konular

Data Sufficiency with Visual and Tabular Contexts

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