Bunuel wrote:
codeblue wrote:
Bunuel wrote:
Official Solution:
Gold depreciated at a rate of \(X\%\) per year between 2000 and 2005. If 1 kg of gold cost \(S\) dollars in 2001 and \(T\) dollars in 2003, how much did it cost in 2002 in terms of \(S\) and \(T\)?
A. \(T\frac{S}{2}\)
B. \(T\sqrt{\frac{T}{S}}\)
C. \(T\sqrt{S}\)
D. \(T\frac{S}{\sqrt{T}}\)
E. \(\sqrt{ST}\)
Step 2: Price of 1kg gold in 2002 - \(S(1-\frac{x}{100})\)
Step 3: Price of 1kg gold in 2003 - \(S(1-\frac{x}{100})^2=T\). So, \((1-\frac{x}{100})=\sqrt{\frac{T}{S}}\)
Step 4: Price of 1kg gold in 2002 - \(S(1-\frac{x}{100})=S*\sqrt{\frac{T}{S}}=\sqrt{ST}\).
Answer: E
I'm not following this last step...
S*\sqrt{\frac{T}{S}}=\sqrt{ST}[/m]. Any help?
From step 2: Price of 1kg gold in 2002 - \(S(1-\frac{x}{100})\).
From step 3: \((1-\frac{x}{100})=\sqrt{\frac{T}{S}}\). Substitute this into the above equation: \(S(1-\frac{x}{100})=S*\sqrt{\frac{T}{S}}=(\sqrt{S})^2*\sqrt{\frac{T}{S}}=\sqrt{ST}\).
Does this make sense?
Step 1: Price of 1kg gold in 2001 - \(S\)
I take the substitution approach
In 2001 , 1 Kg cost $100 .
In 2002 cost is $ 90 .
In 2003 cost is $81
S = 100, T = 81
Now i have subsituted the value in the options.
I checked option a,b,c . All were not tallying.
Option D : T * S/root T = 81 * 100/9 = 900
Option E : root of ST = root of 81*100 =90.
If any better approach is there please highlight.