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Difficult Math Problem #90 - Arithmetic

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800guy: Master | Next Rank: 500 Posts; Posts: 354; Joined: Tue Jun 27, 2006 9:20 pm; Thanked: 11 times; Followed by:5 members

Difficult Math Problem #90 - Arithmetic

by 800guy » Wed Jan 24, 2007 11:31 am

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

from difficult math questions doc. OA coming when some people make responses..

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Source: Beat The GMAT — Problem Solving | Wed Jan 24, 2007 11:31 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

Re: Difficult Math Problem #90 - Arithmetic

by ajith » Sun Apr 01, 2007 9:16 pm

800guy 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

from difficult math questions doc. OA coming when some people make responses..

Total value of the potfolio before increase =210
increase in value ~= 4.2 (2% of 210)

The one stock that increased should be the $70 one because no other possibility is there ( since 15% increase nullifies a 35% decrease in the value)

Now the net increase ~= 4.2

15% increase in $70 = 10.5

now the value curresponding to 35% decrease in script X = X*0.35 =10.5-4.2= 7.3
X=7.3/0.35 =20.85 is close enough to 20

so the changed ones are 70 and 20

E indeed is the answer !!!!

Always borrow money from a pessimist, he doesn't expect to be paid back.

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

by BTGmoderatorRO » Sun Oct 01, 2017 11:15 am

Let us represent the stocks with with changing prices 'f' and 'y', and the stocks with constanr values with 'x', 'y' and 'z'.
Originally, the average price of one stock is = (20+35+40+45+70)/5
=210/5 = 42
now, after the increment /decrements, the average price increased by approximately 2%.
i.e new average = 42+2%+42
=42+0.84
=42.84 .
And the total price of the stocks after changing the prices of some of the them is;
=Average * total number of stocks
=42.84 *85
=214.2
From th representation made above,
f+g+x+y+z=210
or f+g=210-(x+y+z)
Also we can say that:
1.15f+0.65g+x+y+z=214.2
where,
1.15f is the new value of the stock whose value was increased by 15%.
i.e f+15% of f
f+0.15f=1.15f.

Similarly, 0.65 is the new value of the stock whose value was decreased by 35%
i.e g-35% of g
g-0.35=0.65g
Now we can say that,
1.15f+0.65g=214.2-(x+y+z)
By trial and error,we shall assume values for x,y,z,f and g
let x,y,z be 20,35 and 70 respectively and f and g be 40 and 45 respectively.
1.15(40) + 0.65 +(45) = 214.2- (20 +35 + 70)
46+29.25=214.2- 125
75.25 is not equal to 89.2
These values are not even approximately equal
Next try x,y,z =35,40,45 and f,g =70,20
1.15(70)+0.65(20)=214.2-(35+40+45)
80.5+13=214.2-120
93.5 is approximately equal to 94.2
These values are the closest approximately values obtainable.
Therefore,we can conclude that the three constant stocks are priced at
$35, $40 and $45
Hence,option E is correct.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8089; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Difficult Math Problem #90 - Arithmetic

by Scott@TargetTestPrep » Tue Jan 28, 2020 6:01 am

800guy wrote: ↑
Wed Jan 24, 2007 11:31 am
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

from difficult math questions doc. OA coming when some people make responses..

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

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