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Thread: Quantitative reasoning

  1. #1
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    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 !
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  2. #2
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    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
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  3. #3
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    Re: Quantitative reasoning

    Quote Originally Posted by fsiwaju View Post
    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 $\displaystyle 33.\overline{33}\%$.
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