Given that x 5, is x > 1/(x - 5)^2 ? (1) x > 0 (2) x > 10

Target question: Is x > 1/(x-5)² ?
This is a great candidate for rephrasing the target question.
Since (x-5)² is guaranteed to be POSITIVE, we can take the inequality x > 1/(x-5)² and multiply both sides by (x-5)²
When we do this, we get: (x)(x-5)² > 1

So, we can REPHRASE the target question as....
REPHRASED target question: Is (x)(x-5)² > 1?

Statement 1: x > 0
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 10, in which case (x)(x-5)² = (10)(10-5)² = 125. In this case, (x)(x-5)² > 1
Case b: x = 0.01, in which case (x)(x-5)² = (0.01)(0.01-5)² ≈ (0.01)(25) ≈ 0.25 In this case, (x)(x-5)² < 1
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x > 10
If x is greater than 10, it is clear that (x)(x-5)² MUST be greater than 1
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer =

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