Practice GMAT Problem Solving Question

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n5(16k-8)(n-3)=n2; if n does not equal zero, k=
Correct Answer: B
  1. There are two main methods of solving this question.
  2. Algebra
    1. Multiply both sides by n3 to yield n5(16k-8)=n5:
      n5(16k-8)(n-3)=n2
      n5(16k-8)=n5
      16k-8)=1
    2. Cancel the n5 by dividing both sides by n5 to yield 16k-8=1. Dividing by a variable is only possible since the value of that variable is not zero. Dividing by zero would otherwise result in a lost solution to the equation.
    3. 16k-8=1
    4. 16k = 9
    5. k = 9/16
  3. Plugging-In
    1. We are interested in the value of k but we do not know the value of n.
      Since the answer choices we are given are not expressed in terms of n, the value of k must be the same regardless of the value of n.
    2. Since this is true, choose a non-zero value for n such as 1. 1(any integer)=1. So plugging in n=1, the equation simplifies down to 16k-8=1
    3. Add 8 to both sides of the equation to yield: 16k=9
    4. Now divide by 16 to get the value of k=9/16
      Thus, answer B is correct.

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