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

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A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post 19 Jul 2008, 23:15
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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
[Reveal] Spoiler: OA
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post 20 Jul 2008, 00:44
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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] New post 21 Jul 2008, 04:31
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] New post 21 Jul 2008, 05:05
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] New post 21 Jul 2008, 14:09
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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A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post 04 Dec 2008, 17:25
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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
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Re: Statistics: % and logic [#permalink] New post 04 Dec 2008, 22:07
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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: Statistics: % and logic [#permalink] New post 18 Jul 2011, 03:39
is there any other method to do this except to try 35% of atleast 2-3 values and 15% of 2-3 values before guessing the answer? If there is, pls share. Thanks.

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Re: Statistics: % and logic [#permalink] New post 18 Jul 2011, 20:49
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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


Use logic and the calculations involved will be negligible.
Since we have been given that there is an overall increase, the increase should be greater than the decrease. So
15% of A > 35% of B

Now think that 15% of A will be equal to 30% of B if A is twice of B. But 15% of A is greater than 30% of B so A must be greater than twice of B. In fact 15% of A is greater than 35% of B so A must be substantially greater than twice of B. So B has to be 20 because we have values more than twice of 20 (which are 45 and 70). We don't have any values which are more than twice of any other given number (30, 35, 40, 70).

A can be 45 or 70. I would bet on 70 since A has be substantially greater than twice of 20.
Even if I want to confirm, 10% of 20 is 2 so 30% of 20 is 6. 5% of 20 is 1 so 35% of 20 is 7.
15% of A has to be greater than 7. Only 70 satisfies this since 10% of 70 is 7.
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post 03 Dec 2013, 01:50
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
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post 20 Mar 2014, 08:36
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] New post 24 Mar 2014, 03:53
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


Average is 42
2%= .8 (App)
Total in Increase in the portfolio is 4 ( As each stock increases by 0.8 => 5 x 0.8)

Difference between the varying stock prices should be 4

Lets take the first and the most conservative case: 22 decreases by 35% = 7.7
A corresponding increase in a stock price of approx 11 is required to bring the difference in stock prices to 4
We can quickly conclude that 70 ( 7 x 15= 10.5) is as good as it gets...coz any stock other than 22 will have an even greater numerical decrease with a 35% decline in its value and has no share that can maintain the difference of 4 ...as we have already taken the highest increase of 15% in 70
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post 05 Apr 2014, 08:39
@jlgdr: you mean 15x-35y>0

hence (x/y)>(7/3)
when you put x = 70 and y = 20 this equation is satisfied. here x/y is 7/2 > 7/3
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post 01 May 2014, 07:18
sayansarkar wrote:
@jlgdr: you mean 15x-35y>0

hence (x/y)>(7/3)
when you put x = 70 and y = 20 this equation is satisfied. here x/y is 7/2 > 7/3


Not so. Its supposed to be 37y by concept of differentials. See if price of total average rose by 2% and the price of one of the components declined by 35% then the difference is -35--2 = 35+2 = 37

Is this clear?

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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] New post 26 Jul 2014, 19:35
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Re: A certain portfolio consisted of 5 stocks, priced at $20,   [#permalink] 26 Jul 2014, 19:35
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