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An investor purchased 20 shares of certain stock at price of $45.75

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Director
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Joined: 10 Mar 2013
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Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
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An investor purchased 20 shares of certain stock at price of $45.75  [#permalink]

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New post 17 Jan 2016, 04:19
3
3
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

82% (01:54) correct 18% (01:58) wrong based on 232 sessions

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An investor purchased 20 shares of certain stock at price of $45.75 per share. Later this investor purchased 30 more shares at price of $46.25 per share. What was the average price per share that this investor paid for the 50 shares?

1. 45.80
2. 45.95
3. 46.00
4. 46.05
5. 46.20

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Re: An investor purchased 20 shares of certain stock at price of $45.75  [#permalink]

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New post 18 Jan 2016, 12:11
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6
Hi BrainLab,

Yes, you CAN correctly answer this question without doing any long-winded calculations, but you do have to note the particular details in the prompt AND use the answer choices to your advantage.

While the answers appear 'close together', they're really not (relative to what the question is asking.

IF we had an equal number of both types of shares (meaning for every 1 share at $45.75, we'd have 1 share at $46.25), then the average price per share would be $46 exactly. You don't actually have to perform a big calculation to prove that either. Since the first share is 25 cents LESS than $46 and the second share is 25 cents MORE than $46, those differences 'cancel out', leaving us with an average of $46.

The prompt tells us that there are MORE of the $46.25 shares, so the average is clearly going to be greater than $46. That narrows the options down to Answers D and E. However, there are only 20 of the first shares and 30 of the second shares, and Answer E is SO CLOSE to $46.25, that there's no way for that to be the average. There would need to be far more of the second shares (proportionately speaking) to drive the average up to $46.20. Since that's not the case, the answer MUST be Answer D.

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Re: An investor purchased 20 shares of certain stock at price of $45.75  [#permalink]

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New post 17 Jan 2016, 04:32
3
BrainLab wrote:
An investor purchased 20 shares of certain stock at price of $45.75 per share. Later this investor purchased 30 more shares at price of $46.25 per share. What was the average price per share that this investor paid for the 50 shares?

1. 45.80
2. 45.95
3. 46.00
4. 46.05
5. 46.20


Is there some way to avoid intensive calculations ? I've solved it this way.... (at the time I was writing my solution, I saw a much better one :))

\(\frac{45,75*20+30(45,75+0,50)}{50}\) --> \(\frac{50*45,75}{50} + \frac{15}{50}= 45,75+0,3=46,05\)
Answer D
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Re: An investor purchased 20 shares of certain stock at price of $45.75  [#permalink]

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New post 17 Jan 2016, 04:40
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3
BrainLab wrote:
BrainLab wrote:
An investor purchased 20 shares of certain stock at price of $45.75 per share. Later this investor purchased 30 more shares at price of $46.25 per share. What was the average price per share that this investor paid for the 50 shares?

1. 45.80
2. 45.95
3. 46.00
4. 46.05
5. 46.20


Is there some way to avoid intensive calculations ? I've solved it this way.... (at the time I was writing my solution, I saw a much better one :))

\(\frac{45,75*20+30(45,75+0,50)}{50}\) --> \(\frac{50*45,75}{50} + \frac{15}{50}= 45,75+0,3=46,05\)
Answer D


Hi
you dont require to do any intensive calculations if you do by weighted average..
the ratio of shares =2:3 and their price = 45.75:46.25..
the average ratio of total would depend on the ratio of number of shares..
difference in the price = 46.25-45.75=.50..
divide this .50 in the ratio 2:3=.2:.3...
since the number of shares of 46.25 is more, the average will be closer to it...
so average= 46.25- .2=46.05... .2 has come from .2:.3...
D
hope it helps you in reducing your calculations further
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An investor purchased 20 shares of certain stock at price of $45.75  [#permalink]

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New post 07 Apr 2018, 08:47
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\(45.75+\frac{30}{50}*(46.25-45.75)=46.05\)
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Re: An investor purchased 20 shares of certain stock at price of $45.75  [#permalink]

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New post 24 May 2018, 02:29
4
BrainLab wrote:
An investor purchased 20 shares of certain stock at price of $45.75 per share. Later this investor purchased 30 more shares at price of $46.25 per share. What was the average price per share that this investor paid for the 50 shares?

1. 45.80
2. 45.95
3. 46.00
4. 46.05
5. 46.20


Responding to a pm:

The distance between 45.75 and 46.25 is of $0.5. Weights are in the ratio 2:3 so the distance will split in the ratio 3:2 i.e. average will be $46.05.

This is based on the concept that weighted average splits the distance between C1 and C2 is the ratio which is inverse of the ratio of W1 and W2. This is the same concept on which out formulas based:

W1/W2 = (C2 - Cavg) / (Cavg - C1)

I prefer to not use the formula here but just the concept because the formula will involve some calculations.
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Re: An investor purchased 20 shares of certain stock at price of $45.75 &nbs [#permalink] 24 May 2018, 02:29
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