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A certain portfolio consisted of 5 stocks, priced at \$20,  [#permalink]

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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]

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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]

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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)
General Discussion
Retired Moderator Joined: 18 Jul 2008
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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)
Manager  Joined: 04 Apr 2008
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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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Current Student Joined: 12 Jun 2008
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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.

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 Manager  Joined: 11 Mar 2008
Posts: 86
A certain portfolio consisted of 5 stocks, priced at \$20,  [#permalink]

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1
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
SVP  Joined: 29 Aug 2007
Posts: 1918
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

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.
Senior Manager  Joined: 23 Jun 2009
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Re: Portfolio Prices  [#permalink]

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Lets try.

There is a 15% increase in one number and a 35% decrease in other number. But the result is a total increase in sum. This means 15% of a number is slightly bigger that 35%of other number in the set. There is only one possibility for this. That is 70 and 20.
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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 _________________

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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
Cheers
J
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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

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]

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@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]

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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?

Cheers
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A certain portfolio consisted of 5 stocks, priced at \$20,  [#permalink]

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

The above conjecture is incorrect. The right side of the equation is not 0, so making any assumption about the ratio x/y would be poor.

Generalizing the problem we get that a high (H) stock has to increase by 15% and a low (L) stock has to decrease by 35%. (H > L)

Formula looks like: .02*(H + L + Others) = .15*H - .35*L which we can rewrite as .02*Others = .13*H - .37*L.

If the "Other" stocks did not exist you could make an assumption about the ratio of H/L, but since they do, H/L isn't necessarily close to 3.
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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

15% of A = 35% of B. given that the average price of a stock in the portfolio rose by approximately 2%.That means A is slightly more than twice of B.
35% of 20 is 7 and 15% of 70 is 10.5.thus choice E matches.
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Re: A certain portfolio consisted of 5 stocks, priced at \$20,  [#permalink]

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Oski 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 Only 15% gain of 70 and -35% (depreciation) of 20 shall together provide an increase of 2% to all stock options.
Rest all combinations shall provide negative value as in table

+15% -35%

20 : +3 -7
35 : +5.25 -12.25
40 : +6 -14
45 : +6.75 -15.75
70 : +10.5 -24.5
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Re: A certain portfolio consisted of 5 stocks, priced at \$20,  [#permalink]

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jlgdr wrote:
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?

Cheers
J can you please elaborate how the method works?
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Re: A certain portfolio consisted of 5 stocks, priced at \$20,  [#permalink]

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We can consider 102(100+2) as mean of 65(100-35) and 115(100+15) hence by weighted mean method ratio between the changed values X & Y should be x/Y=13/37~ 1/3> the only combination in the given set whose ratio is > 1/3 is 20 & 70,Hence answer E Re: A certain portfolio consisted of 5 stocks, priced at \$20,   [#permalink] 31 Jul 2018, 00:34

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