The quantities S and T are positive and are related by the equation \(S=\frac{K}{T}\), where k is a constant. If the value of S increases by 50 percent, then the value of T decreases by what percent?

A \(25\)%

B \(33 \frac{1}{3}\)%

C \(50\)%

D \(66 \frac{2}{3}\)%

E \(75\)%
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Another approach it to first find some values that satisfy the condition that S = K/T
How about S = 2, K = 2 and T = 1 (since 2 = 2/1)

Now what happens to T if we increase S by 50%?

Well, if we increase 2 (the value of T) by 50%, we get S = 3
K is constant, so K = 2 (still)
What must T equal?

Take S = K/T and plug in the new value of S to get 3 = 2/T (and now solve for T)
To do so, multiply both sides by T to get: 3T = 2
Now divide both sides by 3 to get: T = 2/3

So, the value of T has DECREASED from 1 to 2/3
This represents a 33 1/3% decrease

Answer: B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Basically cross multiply s*t = k

then we should get 3/2 * s * 2/3 *t = k

this way it becomes s * t = k

Since we need 2/3 * t it means we reduced it by 1/3.

So answer choice B