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

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Math Expert
Joined: 02 Sep 2009
Posts: 45360
The quantities S and T are positive and are related by the equation S= [#permalink]

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16 Mar 2016, 05:36
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59% (01:21) correct 41% (01:05) wrong based on 104 sessions

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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%

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Math Expert
Joined: 02 Aug 2009
Posts: 5779
The quantities S and T are positive and are related by the equation S= [#permalink]

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16 Mar 2016, 09:33
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KUDOS
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Bunuel wrote:
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%

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
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Joined: 17 Nov 2014
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Location: India
Re: The quantities S and T are positive and are related by the equation S= [#permalink]

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17 Mar 2016, 02:10
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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Re: The quantities S and T are positive and are related by the equation S= [#permalink]

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24 Apr 2016, 08:13
Bunuel wrote:
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%

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%
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Re: The quantities S and T are positive and are related by the equation S= [#permalink]

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09 Feb 2018, 12:15
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%).

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Re: The quantities S and T are positive and are related by the equation S=   [#permalink] 09 Feb 2018, 12:15
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