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

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BrainLab
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An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   17 Jan 2016, 04:19
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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] New post   18 Jan 2016, 12:11
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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] New post   17 Jan 2016, 04:40
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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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Re: An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   17 Jan 2016, 04:32
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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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An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] 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] New post   24 May 2018, 02:29
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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 [#permalink] New post   02 Jun 2019, 23:46
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Given:

An investor purchased 20 shares of a certain stock at a price of $45.75 per share.

Total money paid for 20 shares = $45.75*20 = $915

Later this investor purchased 30 more shares at a price of $46.25 per share

Total money paid for 30 shares = $46.25*30 = $1387.5

Total money paid for 50 shares = $915 + $1387.5 = $2302.5

The average price per share that this investor paid for the 50 shares = $2302.5/50 = $46.05

The correct answer is D
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Re: An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   06 Oct 2020, 22:01
VeritasKarishma 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


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.



I did not understand this method? Where can I learn about this method?

If the ratio is 2:3 why are we splitting it in 3:2

Please help!

VeritasKarishma
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Re: An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   07 Oct 2020, 03:22
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Approach 1:

Average: \(\frac{Sum }{ Total}\)

The question is based on the weighted average.

Average: \(\frac{[(45.75 * 20) + (46.25 * 30)] }{ 50}\)

=> Average: \(\frac{(915 + 1387.5) }{ 50}\)

=> Average: \(\frac{2,302.5 }{ 50}\)

Average: 46.05

Answer D


Approach 2:

As 20 shares were bought at $45.75 per share and 30 shares are bought at $46.25 per share, then average will be definitely greater than 45.75 because the number of shares and price per share both have increased later.

Increase price: 46.25 - 45.75 = 0.25 per share.

Overall increase: 0.25 * 30 = 15 [Becuase '30' more shares were bought].

This increase of '15' will affect overall 50 shares: \(\frac{15 }{ 50}\) = 0.3

Increase of 0.3 from 45.75 => 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] New post   07 Oct 2020, 11:22
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chetan2u wrote:
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


I prefer this method, so I'd like to understand. I get lost in the above highlighted portion. Please explain. I may be getting lost on the concept of dividing a number into a ratio.
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Re: An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   29 Nov 2020, 17:57
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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

Solution:

The average price per share of the stock was:

(20 x 45.75 + 30 x 46.25) / 50

(915 + 1387.5) / 50

2302.5/50 = $46.05

Answer: 4 or D
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Re: An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   30 Nov 2020, 11:06
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

\(\frac{20*45.75 + 30*46.25}{50}\)

\(= \frac{915 + 1387.5}{50}\)

\(= 46.05\), Answer must be (4)
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Re: An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   19 Dec 2020, 08:52
Hi,

For this question, I used the following method involving weighted averages :

Let's set $46 as our base point
We know that 20/50 (2/5) of our shares are at a unit price of $45.75 so -1/4 from our base point
and that 30/50 (3/5) of our shares are at a unit price of $46.25, so 1/4 more than our base point

2/5*-1/4 = -2/20
3/5*1/4 = 3/20
-2/20+3/20= 1/20 = 5/100 = 0,05

Therefore our AVG price per share is our base point $46+0,05 = 46,05$

Answer D)
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Re: An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   10 Jul 2023, 23:15
Bunuel / GMATNinja looking for more logical approach
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Re: An investor purchased 20 shares of certain stock at price of $45.75 [#permalink] New post   11 Jul 2023, 06:45
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tarunrathi999 wrote:
Bunuel / GMATNinja looking for more logical approach


Hi tarunrathi999,

While the answers to this question appear 'close together', they're really not (relative to what the question is asking) - meaning that you can solve this problem without actually doing much math.

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 type of 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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