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Given that x ≠ 5, is x>{1/(x-5)^2}

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Given that x ≠ 5, is x>{1/(x-5)^2}  [#permalink]

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New post 13 Jul 2016, 09:23
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Given that x ≠ 5, is x>{1/(x-5)^2}

Statement #1: x > 0

Statement #2: x > 10
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Re: Given that x ≠ 5, is x>{1/(x-5)^2}  [#permalink]

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New post 13 Jul 2016, 12:40
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anurag16 wrote:
Given that x ≠ 5, is x > 1/(x-5)²

Statement #1: x > 0

Statement #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: http://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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Given that x ≠ 5, is x>{1/(x-5)^2}  [#permalink]

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New post 13 Jul 2016, 09:57
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anurag16 wrote:
Given that x ≠ 5, is x>{1/(x-5)^2}

Statement #1: x > 0

Statement #2: x > 10


Very tricky one...took time

x>{1/(x-5)^2}

Stat 1 : When X > 0, then X can be 0.01,0.02, 0.05,......0.1,0.5,0.6 ,.... 1,2,3,4,6 ....but not 5

When we substitute

let's say X = 0.01 , then 1/(0.01-5)^2 we get 0.04 , which is greater than 0.01

if X = 6 , if we sub this value in the equation then the result will be less than 6... Two different cases...Insufficient.

Stat 2: When X > 10 onwards , we get result less than X for all cases... Sufficient.

Hence B
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Re: Given that x ≠ 5, is x>{1/(x-5)^2}  [#permalink]

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New post 13 Jul 2016, 10:56
Given Eq: x > 1/(x-5)^2

-> Multiply both sides by (x-5)^2 as it is always positive.
-> Equation becomes : x(x-5)^2 > 1

Statement 1: x>0
x can be any positive number. Say 5.05, this will make x(x-5)^2 less than 1.
But, putting x = 2,3,7..., this will make x(x-5)^2 greater than 1.
So Insufficient.
Statement 2: x>10
Putting x > 10 will always give x(x-5)^2 > 1. Hence, sufficient.

Ans: B
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Re: Given that x ≠ 5, is x>{1/(x-5)^2}  [#permalink]

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Re: Given that x ≠ 5, is x>{1/(x-5)^2}   [#permalink] 09 Feb 2020, 08:48
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