# Practice GMAT Problem Solving Question

n5(16k-8)(n-3)=n2; if n does not equal zero, k=
 A) 2 B) 9/16 C) 1 D) 1/2 E) 5/8
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