The quantities S and T are positive and are related by the equation S=

Question

The quantities S and T are positive and are related by the equation S=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 ¹/₃%
C. 50%
D. 66 ²/₃%
E. 75%

vandyke1234 · Accepted Answer

We can assign numbers:

lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T) 
Now increasing S by 50% gives S=3, K remains constant, so T = 2 (6/2=3)
decrease in T= 1, percent decrease in T = (1/3)*100 = 33.33%
Answer B

EMPOWERgmatRichC · Answer

Hi All,

This question is based on a math 'truism' that's often associated with Rate questions. We're told that S = K/T. Algebraically, that's the same as....

(S)(T) = K

We're told that S and T are both positive and that K is a constant. We're given a hypothetical situation to consider: IF S increases by 50%, by what PERCENT does T decrease....

By increasing S by 50%, we'd have....

(3/2)(S)

...but since K is a CONSTANT, we have to 'offset' that (3/2) with its inverse (in this case, 2/3), which would give us...

(3/2)(S)(2/3)(T) = K 
(3/2)(2/3)(S)(T) = K 
(6/6)(S)(T) = K 
(1)(S)(T) = K 
(S)(T) = K

Since T is now 2/3 of its original value, T has DECREASED by 1/3 (or 33 1/3%).

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

chetan2u · Answer

Hi,

S=K/T..
or K=ST=CONSTANT..
let s=1.5S and t = xT
and so 1.5S*T=K=s*t=1.5S * xT..
so ST=1.5S*xT..
 x=\frac{1}{1.5} ..
therefore  new T=t=T*\frac{1}{1.5} or \frac{2}{3} *T.. 
decrease = \frac{1}{3}t 
%= \frac{100}{3}=33.33% 
B

Badari · Answer

ST = constant 
S inc by 50% i.e new value of S is 1.5 S
1.5S X new T = constant 
Solving we get new T = 66% T
Amount T reduced to keep the value of ST constant is 33%

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ScottTargetTestPrep · Answer

Solution:
 
Notice that S = k/T means ST = k. Since the value of S increases by 50 percent, S has a multiplier of 1.5. Now we can let m = the multiplier of T and create the equation:

(1.5S)(mT) = k

1.5m(ST) = k

1.5m(k) = k

1.5m = 1

m = 1/1.5 = 2/3

Since m, the multiplier of T, is 2/3, we see that the value of T must decrease by 1/3 or 33 ⅓% to maintain the given relationship between S and T.

Alternate Solution:

Let’s let S = 4 and T = 3. We see that ST = k = 12. Now, if S increases by 50%, its new value is 6, and so 6T = k = 12, and we see that T must now equal 2.

Using the percent change equation (New - Old)/Old x 100, the percent change of T is:

(2 - 3)/3 x 100 = -⅓ x 100 = -33.3%, or a 33.3% decrease.

Answer: B

SHoylandBPrep · Answer

Plugging in values is going to be the easiest way to solve this problem. Lots of numbers would work. You could use S = 10, k = 20, and T = 2 because 10 = 20/2.

Now, if you increase S by 50%, you get 15. Use this to find the new T:

> S = k/T

> 15 = 20/T

> 15T = 20

> T = 20/15 = 4/3

So, T goes from 2 to 4/3. Calculate the percent decrease:

> Percent change = Difference/Original × 100%

> Percent change = ⅔ / 2 × 100% = ⅓ × 100% = 33 ⅓%

ScottTargetTestPrep · Answer

Solution:

Notice that S = k/T means ST = k. Since the value of S increases by 50 percent, S has a multiplier of 1.5. Now we can let m = the multiplier of T and create the equation:

(1.5S)(mT) = k

1.5m(ST) = k

1.5m(k) = k

1.5m = 1

m = 1/1.5 = 2/3

Since m, the multiplier of T, is 2/3, we see that the value of T must decrease by 1/3 or 33 ⅓% to maintain the given relationship between S and T.

Alternate Solution:

Let’s let S = 4 and T = 3. We see that ST = k = 12. Now, if S increases by 50%, its new value is 6, and so 6T = k = 12, and we see that T must now equal 2.

Using the percent change equation (New - Old)/Old x 100, the percent change of the value of T, from 3 to 2, is:

(2 - 3)/3 x 100 = -⅓ x 100 = -33.3%, or a 33.3% decrease.

Answer: B

Kinshook · Answer

The quantities S and T are positive and are related by the equation S=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?

S' = K/T' = K/1.5T = 2K/3T = (1-1/3)K/T

IMO B

Archit3110 · Answer

Given s=k/t
Let s 100 ;
t =k/100
Later with 50% increase of S we get
t=k/150
% increase
(k/100-k/150)k/100
3-2/3;1/3 ;33.33%
Option B

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Iotaa · Answer

It's a GRE Official Mock Question. The main point to focus: Value of T decreases by what percent, not the new value of T.

By equating ST= 1.5S X a T
 => T= 2/3 or 66.66.

So the reduction in value will be 100-66.66, which is 33.33. hence B is the answer

saurvan · Answer

Assign numbers to all of S, K , T.

bumpbot · Answer

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