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x is a positive number. Is x > 1?

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by Max@Math Revolution » Thu May 23, 2019 12:20 am

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[GMAT math practice question]

x is a positive number. Is x > 1?

1) √x > x
2) x^3 - x < 0
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun May 26, 2019 5:29 pm
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

In inequality questions, the law "Question is King" tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient

Condition 1)
√x > x
=> x > x^2 by squaring
=> x^2 - x < 0
=> x(x-1) < 0
=> 0 < x < 1
Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)
x^3 - x < 0
=> x(x^2-1) < 0
=> (x+1)x(x-1) < 0
=> x < -1 or 0 < x < 1
=> 0 < x < 1 since x is positive.
Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.


Therefore, D is the answer.
Answer: D
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