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20 Jul 2008, 00:15
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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
A. 20, 35, 70
B. 20, 45, 70
C. 20, 35, 40
D. 35, 40, 70
E. 35, 40, 45
snaps
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
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.
Check this post on Percentages:
https://anaprep.com/arithmetic-simple-a ... rcentages/
and this video: https://youtu.be/HxnsYI1Rws8
20 Jul 2008, 01:44
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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)
- 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)
