# Quantitative reasoning

• Jan 6th 2013, 05:59 AM
fsiwaju
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 !
• Jan 6th 2013, 06:51 AM
skeeter
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
• Jan 6th 2013, 07:10 AM
abender
Re: Quantitative reasoning
Quote:

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 $S$ and $T$ are positive and $S=\frac{k}{T}$ , then $k$ must be a positive constant.
So, let's assign positive numerical values to $S$, $T$, and $k$ such that $S=\frac{k}{T}$.
For example, let $S=10$, $k=1000$ and $T=100$.

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

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

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