An investor purchased 20 shares of a certain stock at a price of $45.7

Question

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

A. $45.80
B. $45.95
C. $46.00
D. $46.05
E. $46.20

EMPOWERgmatRichC · Accepted Answer

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.

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

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

BrainLab · Answer

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

banarsumboro07 · Answer

45.75+\frac{30}{50}*(46.25-45.75)=46.05

KarishmaB · Answer

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.

AyushCrackVerbal · Answer

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

Sri07 · Answer

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

MathRevolution · Answer

Approach 1:

Average:  \frac{Sum }{ Total}

The question is based on the weighted average.

Average:  \frac{  }{ 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  .

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

Asariol · Answer

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.

ScottTargetTestPrep · Answer

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

Abhishek009 · Answer

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

= \frac{915 + 1387.5}{50}

= 46.05 , Answer must be (4)

Sabby · Answer

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)

tarunrathi999 · Answer

Bunuel  /  GMATNinja  looking for more logical approach

EMPOWERgmatRichC · Answer

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. GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com www.empowergmat.com

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

An investor purchased 20 shares of a certain stock at a price of $45.7

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

An investor purchased 20 shares of a certain stock at a price of $45.7

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards