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An investor can sell her MicroTron sock for 36$ per share and

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Joined: 05 Sep 2013
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An investor can sell her MicroTron sock for 36$ per share and [#permalink]

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New post 17 Nov 2014, 13:30
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An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 52$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?


A) 52
B) 75
C) 92
D) 136
E) 184
[Reveal] Spoiler: OA
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Manager
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Posts: 147
Location: United States
Concentration: Finance, Strategy
GMAT 1: 700 Q47 V39
Re: An investor can sell her MicroTron sock for 36$ per share and [#permalink]

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New post 17 Nov 2014, 13:55
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MicroTron stock: $36/share
Dynaco stock: $52/share

Total revenue from selling 300 shs at $40 avg price per share: 300 * $40/share = $12,000

So the investor sold x shares of MicroTron stock at $36/share and (300 - x) shares of Dynaco stock at $52/share for a total of $12,000 in sales. We can express the equation as follows:

$36x + $52(300 - x) = $40 * 300

which simplifies to:

$36x + $15,600 - $52x = $12,000

Simplify further:

$3,600 = 16x

x = 225

Plug in x = 225 into the equation we derived to figure out she sold 300 - 225 = 75 shs of Dyanco.

Hope this helps!
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Re: An investor can sell her MicroTron sock for 36$ per share and [#permalink]

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New post 17 Nov 2014, 21:54
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NATABERI wrote:
An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 52$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?


A) 52
B) 75
C) 92
D) 136
E) 184


Use the weighted averages formula discussed here: http://www.veritasprep.com/blog/2011/03 ... -averages/

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (52 - 40)/(40 - 36) = 12/4 = 3/1 = Number of MicroTron stocks/Number of Dynaco stocks

So for every 3 MicroTron stock, she sold 1 Dynaco stock.
So out of 300 total stocks, (1/4)th i.e. 300/4 = 75 must be Dynaco stock.

Answer (B)
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Re: An investor can sell her MicroTron sock for 36$ per share and [#permalink]

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New post 18 Nov 2014, 01:12
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Say stock of Dynaco shares = x,

then stock of MicroTron shares = (300-x)

Setting up the equation

36(300-x) + 52x = 40*300

\(x = \frac{300}{4} = 75\)

Answer = B
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An investor can sell her MicroTron sock for 36$ per share and [#permalink]

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New post 20 Dec 2014, 10:08
NATABERI wrote:
An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 52$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?


A) 52
B) 75
C) 92
D) 136
E) 184


Hi,
yeah, this one can be solved quicky using the weighted average approach.

Avg = 40 $
MicroTron stock = 36$
Dynaco stock = 52$

Arrange this on a number line for clarity:

36----40------------52

Note:Notice the average is closer to 36$. So that means there will be more no. of MicroTron stocks sold.

According to to the weighted average approach, the ratio of the quantities will be opposite of the distance from the avergae i.e. ratio of MicroTron stock : Dynaco stock = 12:4
Now solve it as a ratio problem.
Lets say the unknown multiplier is 'x'
so we have 12x + 4x = 300
x = 75/4
Therefore 4x = 4 * (75/4) = 75.

For more information on weighted averages, check out the quants link below:
consolodited-quant-guides-of-forum-most-helpful-in-preps-151067.html#p1217652

Thanks!
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Re: An investor can sell her MicroTron sock for 36$ per share and [#permalink]

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Re: An investor can sell her MicroTron sock for 36$ per share and   [#permalink] 25 Dec 2017, 22:36
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