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In a certain stock portfolio with 500 shares of different stocks, the

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New post 26 Dec 2017, 00:18
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In a certain stock portfolio with 500 shares of different stocks, the average (arithmetic mean) value of a share of the stocks is $11. If the value of a share of one of the stocks, of which the portfolio contains 300 shares, decreases by $1 what will be the average value of the stocks in the portfolio?

A. $17.30
B. $10.90
C. $10.83
D. $10.40
E. $9.80

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Re: In a certain stock portfolio with 500 shares of different stocks, the  [#permalink]

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New post 26 Dec 2017, 01:45
Bunuel wrote:
In a certain stock portfolio with 500 shares of different stocks, the average (arithmetic mean) value of a share of the stocks is $11. If the value of a share of one of the stocks, of which the portfolio contains 300 shares, decreases by $1 what will be the average value of the stocks in the portfolio?

A. $17.30
B. $10.90
C. $10.83
D. $10.40
E. $9.80


This is a question involving a ratio (between portfolios) and a percent increase (in stock value).
We'll solve it using the logic of ratios, a Logical approach.

300/500 shares = 3/5 of the portfolio decreased by $1.
Then we should expect the average price to decrease by 3/5 of $1 = $0.60
Our new price is 11 - 0.60 = $10.4
(D) is our answer.
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Re: In a certain stock portfolio with 500 shares of different stocks, the  [#permalink]

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New post 26 Dec 2017, 02:37
Bunuel wrote:
In a certain stock portfolio with 500 shares of different stocks, the average (arithmetic mean) value of a share of the stocks is $11. If the value of a share of one of the stocks, of which the portfolio contains 300 shares, decreases by $1 what will be the average value of the stocks in the portfolio?

A. $17.30
B. $10.90
C. $10.83
D. $10.40
E. $9.80


We have 500 shares with average of $11. So total portfolio value\(= $11*500= $5,500\).
Value of 300 shares decreased by $1 so new portfolio value=\($5,500- $1*300= $5,200\).

New Average value of stocks= \($5,200/ 500= $10.40\). Hence D.
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Re: In a certain stock portfolio with 500 shares of different stocks, the  [#permalink]

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New post 26 Dec 2017, 02:49
Mean 11 * 500=5500

New mean,

300*10+200*11=5200

5200/500= 10.4

And:d

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Re: In a certain stock portfolio with 500 shares of different stocks, the  [#permalink]

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New post 27 Dec 2017, 05:43
Bunuel wrote:
In a certain stock portfolio with 500 shares of different stocks, the average (arithmetic mean) value of a share of the stocks is $11. If the value of a share of one of the stocks, of which the portfolio contains 300 shares, decreases by $1 what will be the average value of the stocks in the portfolio?

A. $17.30
B. $10.90
C. $10.83
D. $10.40
E. $9.80


\(Average=\frac{Sum}{Quantity}\)

\(Average.Before=\frac{500*11}{500}=11\)

\(Average.After=\frac{500*11}{500}-\frac{300*1}{500}=11-\frac{3}{5}=10.40\)

(D) is the answer.
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Re: In a certain stock portfolio with 500 shares of different stocks, the  [#permalink]

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New post 27 Dec 2017, 11:17
Bunuel wrote:
In a certain stock portfolio with 500 shares of different stocks, the average (arithmetic mean) value of a share of the stocks is $11. If the value of a share of one of the stocks, of which the portfolio contains 300 shares, decreases by $1 what will be the average value of the stocks in the portfolio?

A. $17.30
B. $10.90
C. $10.83
D. $10.40
E. $9.80


Total value of 500 shares is $ 5500

Since the value of 300 shares, decreases by $1, net decrease in value is - $ 300

So, The effective total value of 500 shares is $ 5200

The average value of the stocks in the portfolio is = \(\frac{5200}{500}\) = \($ 10.4\)

Answer will be (D) \($10.40\)
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