Practice GMAT Problem Solving Question
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n^{5}(16k8)(n^{3})=n^{2}; if n does not equal zero, k=
Correct Answer: B
 There are two main methods of solving this question.

Algebra
 Multiply both sides by n^{3} to yield n^{5}(16k8)=n^{5}:
n^{5}(16k8)(n^{3})=n^{2}
n^{5}(16k8)=n^{5}
16k8)=1  Cancel the n^{5} by dividing both sides by n^{5} to yield 16k8=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.
 16k8=1
 16k = 9
 k = 9/16
 Multiply both sides by n^{3} to yield n^{5}(16k8)=n^{5}:

PluggingIn
 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.  Since this is true, choose a nonzero value for n such as 1. 1^{(any integer)}=1. So plugging in n=1, the equation simplifies down to 16k8=1
 Add 8 to both sides of the equation to yield: 16k=9
 Now divide by 16 to get the value of k=9/16
Thus, answer B is correct.
 We are interested in the value of k but we do not know the value of n.
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