1. ## Quantitative reasoning

Hello,

another quantitative reasoning question from my GRE booklet that I desperately need help with :

The quantities of S and T are positive and related by the equation S= k/T where k is a constant. If the value of S increases by 50%, then the value of T decreases by what percent?

a) 25%
b) 33 1/3 %
c) 50%
d) 66 2/3 %
e) 75%

Any suggestions appreciated !

2. ## Re: Quantitative reasoning

pick some easy values to work with ...

let S = 2

k = 6

T = 3

T = k/S

3 = 6/2

increase S by 50% ...

T = 6/3

T = 2

T changes from 3 to 2 ... a 33 1/3 % decrease

3. ## Re: Quantitative reasoning

Originally Posted by fsiwaju
Hello,
The quantities of S and T are positive and related by the equation S= k/T where k is a constant. If the value of S increases by 50%, then the value of T decreases by what percent?

a) 25%
b) 33 1/3 %
c) 50%
d) 66 2/3 %
e) 75%
If $\displaystyle S$ and $\displaystyle T$ are positive and $\displaystyle S=\frac{k}{T}$ , then $\displaystyle k$ must be a positive constant.
So, let's assign positive numerical values to $\displaystyle S$, $\displaystyle T$, and $\displaystyle k$ such that $\displaystyle S=\frac{k}{T}$.
For example, let $\displaystyle S=10$, $\displaystyle k=1000$ and $\displaystyle T=100$.

These values work for $\displaystyle S=\frac{k}{T}$.

Then,
$\displaystyle 1.5S=\frac{k}{T_*} \implies 1.5\left(10\right)=\frac{1000}{T_*} \implies T_* = \frac{1000}{15} = 66.\overline{66}$

$\displaystyle T=100$ and $\displaystyle T_*=66.\overline{66}$, which is a decrease of $\displaystyle 33.\overline{33}\%$.