An SAT style question?

Question

At the beginning of the year, the price of stock A was 35% greater than the price of stock B. Over the course of the year, the price of stock A doubled while the price of stock B decreased by 10%. At the end of the year, how many times greater was the price of stock A than the price of stock B?

Answer 1

Much easier to deal with percentage problems when you just pick numbers

 

Initially: 

 

Stock A: 135

Stock B: 100

 

End of the year: 

Stock A: 270

Stock B: 90

 

At the end of year, Stock A is 3 times as much as Stock B.  When  you see a percentage problem on the SAT you need to work with 100 as a basis.  

Answer 2

Hi Justin,

 

You can see that first A = (B+B*(0.35)) = B*(1.35), then you know that the price of the stock A doubled:

 

1) A_new = 2*A =(2)(B)(1.35).

 

Also you know that stock B has decreased by 10%:

 

B_new = B - B(0.1) = B(0.9).

 

Now you solve for B:

 

B = B_new / 0.9

 

replacing B in 1):

 

A_new = (2)( B_new / 0.9)(1.35) = (3)(B_new)

 

It means that A_new is three times B_new.

Answer 3

Justin,

 

Assume price of stock B is $x at start of the year

Price of stock A at start of the year = (135/100)*x = 1.35x

 

At end of the year price of stock A doubled, i.e. 2*1.35x = 2.7x

 

While price of stock B reduced by 10%, i.e (90/100)x = 0.9x

 

At end of year stock A/stock B = 2.7x/(0.9x) = 3

 

Stock A is 3 times greater