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Is 1+x+x^2+x^3+x^4<1/(1-x)? 1) x>0 2) x<1 * A so

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by Max@Math Revolution » Mon Mar 21, 2016 3:32 am
Is 1+x+x^2+x^3+x^4<1/(1-x)?

1) x>0
2) x<1


* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Mar 23, 2016 5:42 pm
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is 1+x+x^2+x^3+x^4<1/(1-x)?

1) x>0
2) x<1


The question is (1-x^5)/(1-x)<1/(1-x)? and -x^5/(1-x)<0?, x^5/(x-1)<0? is derived when delete 1/(1-x) from the both equations of 1/(1-x)-x^5/(1-x)<1/(1-x)?. When you multiply (x-1)^2 to the both equations, x^5(x-1)<0? is derived. Divide it with x^4 and it becomes x(x-1)<0?. That is, 0<x<1? is derived, which makes C the answer.
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