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

Question

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

KarishmaB · Accepted Answer

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

Oski · Answer

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)

bigfernhead · Answer

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.

apurva1985 · Answer

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

Oski · Answer

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

GMAT TIGER · Answer

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.

maliyeci · Answer

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.

WoundedTiger · Answer

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:

jlgdr · Answer

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

ScottTargetTestPrep · Answer

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

Dumsy_1711 · Answer

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

Dereno · Answer

The original average of the five stock prices is around 42, which lies close to the three middle values:  35, 40, and 45 .

Since the average increases by only about  2% , the overall change in the total value of the portfolio must be  small . That’s, the change must not be too high for the averages to shift (either left or right). 
 
 Large percentage changes (+15% and −35%) applied to  middle values  (near the mean) would shift the average  more significantly , making it difficult to end up with only a slight (2%) average increase.

To keep the average almost unchanged, the large percentage changes need to be applied to the  extreme values  (20 and 70), because the increase from the lower extreme (20) and decrease from the higher extreme (70) will help us land nearer to the mean values compared to the earlier situation.
 
 So, 35, 40, and 45 should remain unaffected.

Option E

Wadree · Answer

All stocks $ 20 , $ 35 , $ 40 , $ 45 and $ 70 ......
Average price of any stock increased by 2 % approximately.......
So total increase = ( 20 + 35 + 40 + 45 + 70 ) × 2 % = $ 4.2 
Now..... One stock price decreased 35 % and another stock price increased 15 % ...... Which ultimately increased all stock price....... So the stock that increased in price must be more expensive than the stock that decreased in price.......
Let.....we wanna make highest increase possible.....so we'll take $ 70 stock as the increasing one and $ 20 stock as the decreasing one......
So....... increased price = 15 % of $ 70 = $ 10.5
And...... decreased price= 35 % of $ 20 = $ 7
So..... ultimate increase = $ 10.5 - $ 7 = $ 3.5
But...... we need to make ultimate increase of approximately $ 4.2 ........but highest ultimate increase we can get is $ 3.5 .......so $ 20 decreased and $ 70 increased is the only closest way to get required ultimate increase......... So the constant stocks were $ 35 ..... $ 40 ...... $ 45 ........

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

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

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