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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink]
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How did you know which price to increase and decrease?

Is it by process of elimination (trying each one by one), or is there a quicker method.

Oski wrote:
Make the smallest decrease and the highest increase, and you have:

- for the smallest: 35% of $20 = $7 decrease
- for the highest: 15% of $70 = $10.5 increase

==> maximum increase of the portfolio is $3.5 total

Total value of the portfolio was $20+$35+$40+$45+$70 = $210

So the maximun increase corresponds to 3.5/210 = 1.7%

You cannot be closer to 2%, thus it is $20 that decrease and $70 that increase

==> Answer is (E)
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink]
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generally we start with the midlle terms and then you move on one side......But depends upon the experience that one selects the limits.....POE
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink]
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bigfernhead wrote:
How did you know which price to increase and decrease?

Is it by process of elimination (trying each one by one), or is there a quicker method.

I decreased the minimum and increased the maximum, therefore the gap I got is the biggest we can get. And it is still not sufficient to reach the 2% mark : so this is the answer.

A more general method if you do not see it from the begining is as follow :

- compute 2% of the total (here 210*2% = 4.2)

- write down the five numbers and compute for each one what it means to increase it by 15% or decrease it by 35%

20 : +3 ; -7
35 : +5.25 ; -12.25
40 : +6 ; -14
45 : +6.75 ; -15.75
70 : +10.5 ; -24.5

- then, "play" with the 10 numbers you get to be as close as possible to this 4.2 ;)
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Re: Statistics: % and logic [#permalink]
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snaps wrote:
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


E) 35, 40, 45

It has to be E cuz the 2% of of the portfolio is approx 4.00 and the diff between 15% of 70 and 35% of 20 = 3.50. so this is the most closest.
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Re: Portfolio Prices [#permalink]
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enigma123 wrote:
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 stock 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, and $70
(B) $20, $45, and $70
(C) $20, $35, and $40
(D) $35, $40, and $70
(E) $35, $40, and $45

Unfortunately, the official answer is not provided. Can someone please help?

This is a pure trial and error question. You should try 5*4 options.

But there may be a short cut.
Increase of one by 15% and decrease of other buy 35% means a little increase. Thus, the increasing one must be at least 2,3 times of the decreasing one. There is only one probability that is 20 and 70. 70*0,15-20*0,35=3,5 is 1,7 percent of original sum.

That is to say, answer is E.
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink]
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snaps wrote:
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


Sum of price of all stocks : $ 210
Avg price : $ 42

The average price of the stock goes up by 2% of Avg stock price which is $ 0.84-------> This indicates the total increase in the sum is 0.84*5 = $ + 4.20

from the Q we can say that since the avg stock price has gone up therefore 0.15A - 0.35B >0. A has to be greater than B and thus we have

or 0.15A- 0.35B ~ 4.2$
Now 35% of 20 = 7 and 15% of 70 = 10.5 Diff : 3.5
0.15*35 = ~ 5.25 and 15 % of 70 =10.5 Diff: ~ 5
0.15*35= 5.25. and 15% of 45 = 6.75, Diff~ 1.5

For any other combination
ex B = 35 and 0.35 B = 12.25 and A =0.15*70 = 10.5 and the difference between A and B is negative and as B increase the the difference of A and B will become more negative.

Hence Ans option E. The values which are constant
:wink:
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink]
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Or one can use differentials

13x - 37y = 0 therefore X is close to 3 times Y

So the only possibilities that even comes close to this is that X = 70 and Y=20

Therefore, the stocks that remain unchanged are the middle three values: 35, 40,45

Hope this clarifies
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink]
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arjtryarjtry wrote:
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


If the average price of the stocks rose by approximately 2%, then a stock with a higher price (for example, $45 or $70) must have increased by 15%, while a stock with a lower price (for example, $20 or $35) must have decreased by 35%. So let’s guess that the stock with the highest price has increased by 15%, and the stock with the lowest price has decreased by 35%. We need to verify that this is indeed the case.

Old average price = (20 + 35 + 40 + 45 + 70)/5 = 210/5 = $42

New average price = (20 x 0.65 + 35 + 40 + 45 + 70 x 1.15) = 213.5/5 = $42.7

Now let’s calculate the percent change:

(42.7 - 42)/42 x 100 = 0.7/42 x 100 = 1.67% ≈ 2%

Therefore, we do see that the stock with the highest price has increased by 15%, and the stock with the lowest price has decreased by 35%. That is, the three stocks whose prices remain constant are $35, $40, and $45.

Answer: E
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink]
jlgdr wrote:
Or one can use differentials

13x - 37y = 0 therefore X is close to 3 times Y

So the only possibilities that even comes close to this is that X = 70 and Y=20

Therefore, the stocks that remain unchanged are the middle three values: 35, 40,45

Hope this clarifies
Cheers
J



How did you get 13x-37y = 0?
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