Investment, Interest rates and formula

[pepeprepa]

An investor purchased a share of non-dividend-paying stock for p dollars on Monday. For a certain number of days, the value of the share increased by r percent per day. After this period of constant increase, the value of the share decreased the next day by q dollars and the investor decided to sell the share at the end of that day for v dollars, which was the value of the share at that time. How many working days after the investor bought the share was the share sold, if
r= 100 * ( sqrt( (v+q)/p ) -1 ) ?
A) Two working days later.
B) Three working days later.
C) Four working days later.
D) Five working days later.
E) Six working days later

[sudhir3127]

An investor purchased a share of non-dividend-paying stock for p dollars on Monday. For a certain number of days, the value of the share increased by r percent per day. After this period of constant increase, the value of the share decreased the next day by q dollars and the investor decided to sell the share at the end of that day for v dollars, which was the value of the share at that time. How many working days after the investor bought the share was the share sold, if
r= 100 * ( sqrt( (v+q)/p ) -1 ) ?
A) Two working days later.
B) Three working days later.
C) Four working days later.
D) Five working days later.
E) Six working days later

For me its B

Assuming X days ...

i am using Compound Interest.

v = p (1+r/100)^x - q

if i solve for r i get

r=(xth root of (v +q)/p -1 )*100.......................................1

Question stem tells us that

r= 100 * ( sqrt( (v+q)/p ) -1 )...........................................2

substitute 2 in 1

we get
100 * ( ( (v+q)/p ) -1 )^1/2 = [(v +q)/p -1 )]^1/x*100

from this we know X =2

Thus the shares rose for 2 days and on the following day they fell and the investor sold in on the next day

thus its 2+ 1 days = 3

hope that helps..

[pepeprepa]

That's it, I think there is only one way.

[Edthesock]

Wow... I spent so long on this. Very good job Sudhir, very impressive, especially if you did it in 2 minutes like a standard GMAT question!

I'm okay for solving x to get 2 days in the compound interest formula, but how do you know the stock was sold 1 day later?

[sudhir3127]

Wow... I spent so long on this. Very good job Sudhir, very impressive, especially if you did it in 2 minutes like a standard GMAT question!

I'm okay for solving x to get 2 days in the compound interest formula, but how do you know the stock was sold 1 day later?

Because the question says
"After this period of constant increase, the value of the share decreased the next day by q dollars and the investor decided to sell the share at the end of that day for v dollars"

this period here is 2 days
next day would be day 3.

hope this clear .. do let me know if u need any help ..