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A certain portfolio consisted of 5 stocks, priced at $20,

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GK_Gmat
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A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   03 Nov 2007, 05:26
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A
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E

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A certain portfolio consisted of 5 stocks, priced at $20, $35, $40, $45 and $70, respectively. On a given day, the price of one stock increased by 15%, while the price of another decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant?

A) 20, 35, 70

B) 20, 45, 70

C) 20, 35, 40

D) 35, 40, 70

E) 35, 40, 45


The technique I'm using is not giving the correct answer; the technique that is giving the correct answer, I do not understand. Please show your work and explain your answer.



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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   03 Nov 2007, 06:00
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1. Find what is 2% increase in $ for an average stock (for all stocks).

2. (20+35+40+45+70)*0.02 = 4.2$

3. You know that to yield 4.2$ for all five stocks one stock rose 0.15 and one fell 0.35.

4. 0.15x-0.35y = 4.2 ---> 0.05(3x-7y) = 4.2 ---> 3x-7y = 84

5. The only two stocks that can give you the closest solution for x,y are 70 and 20.

the answer is (E)
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   03 Nov 2007, 06:53
KillerSquirrel wrote:
1. Find what is 2% increase in $ for an average stock (for all stocks).

2. (20+35+40+45+70)*0.02 = 4.2$

3. You know that to yield 4.2$ for all five stocks one stock rose 0.15 and one fell 0.35.

4. 0.15x-0.35y = 4.2 ---> 0.05(3x-7y) = 4.2 ---> 3x-7y = 84

5. The only two stocks that can give you the closest solution for x,y are 70 and 20.

the answer is (E)


That was good! :)
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   03 Nov 2007, 10:15
1. Find what is 2% increase in $ for an average stock (for all stocks).

2. (20+35+40+45+70)*0.02 = 4.2$

3. Now we get the greatest diff when there is 15% increase on 70 and 35% decrease on 20 which is 10.5 - 7 = 3.5. For all other options it will be less then 3.5.

Therefore I agree with E
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   03 Nov 2007, 10:28
KillerSquirrel wrote:
1. Find what is 2% increase in $ for an average stock (for all stocks).

2. (20+35+40+45+70)*0.02 = 4.2$

3. You know that to yield 4.2$ for all five stocks one stock rose 0.15 and one fell 0.35.

4. 0.15x-0.35y = 4.2 ---> 0.05(3x-7y) = 4.2 ---> 3x-7y = 84

5. The only two stocks that can give you the closest solution for x,y are 70 and 20.

the answer is (E)


KS: Here's where I'm having trouble. The stem states that 'the average price of a stock in the portfolio rose by approximately 2%'. So why are you multiplying the sum (210) by .02 and not the average (210/5=42) by .02?

Thanks.
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   03 Nov 2007, 10:41
GK_Gmat wrote:
KillerSquirrel wrote:
1. Find what is 2% increase in $ for an average stock (for all stocks).

2. (20+35+40+45+70)*0.02 = 4.2$

3. You know that to yield 4.2$ for all five stocks one stock rose 0.15 and one fell 0.35.

4. 0.15x-0.35y = 4.2 ---> 0.05(3x-7y) = 4.2 ---> 3x-7y = 84

5. The only two stocks that can give you the closest solution for x,y are 70 and 20.

the answer is (E)


KS: Here's where I'm having trouble. The stem states that 'the average price of a stock in the portfolio rose by approximately 2%'. So why are you multiplying the sum (210) by .02 and not the average (210/5=42) by .02?

Thanks.




let me handle this KS:

The orignal average comes out to be 42 as u know.
Now 2% of 42 = 0.84
So the total average is now 42.84
When we multiply the average (42.84) by 5 we get 214.2
which is 4.2 more then the orignal total (210)
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   03 Nov 2007, 10:54
GK_Gmat wrote:
KillerSquirrel wrote:
1. Find what is 2% increase in $ for an average stock (for all stocks).

2. (20+35+40+45+70)*0.02 = 4.2$

3. You know that to yield 4.2$ for all five stocks one stock rose 0.15 and one fell 0.35.

4. 0.15x-0.35y = 4.2 ---> 0.05(3x-7y) = 4.2 ---> 3x-7y = 84

5. The only two stocks that can give you the closest solution for x,y are 70 and 20.

the answer is (E)


KS: Here's where I'm having trouble. The stem states that 'the average price of a stock in the portfolio rose by approximately 2%'. So why are you multiplying the sum (210) by .02 and not the average (210/5=42) by .02?

Thanks.


It's the same thing, but its easier to work with the sum rather then the average.

assume three stocks (10, 20, 30) ---> 30 decreased by 50%

sum = 60 ---> average = 20 ---> 2% sum = 0.12 ---> 2% average = 0.04 (i.e. 0.12/3)

after 50% decrease

sum = 45 ---> average = 15 ---> 2% sum = 0.09 ---> 2% average = 0.03 (0.09/3)

:)
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   03 Nov 2007, 10:54
sportyrizwan wrote:
GK_Gmat wrote:
KillerSquirrel wrote:
1. Find what is 2% increase in $ for an average stock (for all stocks).

2. (20+35+40+45+70)*0.02 = 4.2$

3. You know that to yield 4.2$ for all five stocks one stock rose 0.15 and one fell 0.35.

4. 0.15x-0.35y = 4.2 ---> 0.05(3x-7y) = 4.2 ---> 3x-7y = 84

5. The only two stocks that can give you the closest solution for x,y are 70 and 20.

the answer is (E)


KS: Here's where I'm having trouble. The stem states that 'the average price of a stock in the portfolio rose by approximately 2%'. So why are you multiplying the sum (210) by .02 and not the average (210/5=42) by .02?

Thanks.




let me handle this KS:

The orignal average comes out to be 42 as u know.
Now 2% of 42 = 0.84
So the total average is now 42.84
When we multiply the average (42.84) by 5 we get 214.2
which is 4.2 more then the orignal total (210)


Thanks - I'm just not as fast :wink:
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post   23 Aug 2016, 00:47
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink]
23 Aug 2016, 00:47
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