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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]  04 Dec 2008, 17:25
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64% (03:18) correct 35% (03:04) wrong based on 39 sessions
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: Statistics: % and logic [#permalink]  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]  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.

Nice question!
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Re: Statistics: % and logic [#permalink]  18 Jul 2011, 20:49
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Expert's post
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: Statistics: % and logic [#permalink]  18 Jul 2011, 23:20
Thanks Karishma!!!
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Re: Statistics: % and logic [#permalink]  18 Jul 2011, 23:29

Karishma, Thanks for the explanation!!
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Re: A certain portfolio consisted of 5 stocks, priced at \$20, [#permalink]  02 Dec 2013, 13:07
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Re: A certain portfolio consisted of 5 stocks, priced at \$20, [#permalink]  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] 03 Dec 2013, 01:50
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