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Math Help - [SOLVED] find the value of k

  1. #1
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    [SOLVED] find the value of k

    Hey again,
    This is on page 851 #15 on the SAT OG Book.

    If \frac{n}{n-1} multiply \frac{1}{n} multiply \frac{n}{n+1} = \frac{5}{k}
    for positive integers n and k, what is the value of k?

    a) 1
    b)5
    c) 24
    d) 25
    e)26

    THanks in advance
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by fabxx View Post
    Hey again,
    This is on page 851 #15 on the SAT OG Book.

    If \frac{n}{n-1} multiply \frac{1}{n} multiply \frac{n}{n+1} = \frac{5}{k}
    for positive integers n and k, what is the value of k?

    a) 1
    b)5
    c) 24
    d) 25
    e)26

    THanks in advance
    when you multiply the left side out, you get \frac{n}{n^2-1}

    So you end up with \frac{n}{n^2-1}=\frac{5}{k}

    For these fractions to be equal, n=5, and k=n^2-1

    So k=\dots

    I'm sure you take it from here.

    --Chris
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  3. #3
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    Hello, fabxx!

    If \frac{n}{n-1} \cdot \frac{1}{n} \cdot \frac{n}{n+1} \:= \:\frac{5}{k} for positive integers n and k, what is the value of k ?

    . . (a)\;1 \qquad(b)\:5 \qquad (c)\;24 \qquad (d)\;25 \qquad (e)\;26

    We have: . \frac{n}{n^2-1} \:=\:\frac{5}{k}

    We see that n is either 5 or a multiple of 5 (and the fraction is reduced).


    The fraction is: . \frac{n}{(n-1)(n+1)}
    It is comprised of three consecutive numbers, like \frac{7}{6\cdot8}\,\text{ or }\,\frac{10}{9\cdot11}
    . . Hence, the fraction cannot be reduced.

    Therefore: . n = 5\quad\Rightarrow\quad \frac{5}{5^2-1} \:=\:\frac{5}{k} \quad\Rightarrow\quad k = 24 ... answer (c)

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