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

Question

Given that  x ≠ 5 , is  x > \frac{1}{(x - 5)^{2}}  ?

(1)  x > 0

(2)  x > 10

BrentGMATPrepNow · Accepted Answer

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 = B Related Videos https://www.youtube.com/watch?v=MyG1K3ee69w https://www.youtube.com/watch?v=Od98BOicIq4

msk0657 · Answer

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

shashank1tripathi · Answer

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

Fdambro294 · Answer

Any other strategy to answer the question aside from number plugging?

Or is this question a prime candidate for number plugging

Posted from my mobile device

AdikGoel · Answer

@e-gmat Can you provide a solution to this question in the wav@y line method approach?

thakurarun85 · Answer

1) x>0
x-5>-5
(x-5)^2>0 (please check why)
x>0
=>
x(x-5)^2>0 
now put x=1/100 then it is <1 and when x=25 it is >1.

2) x>10
x-5>5
(x-5)^2>25
x>10
x*(x-5)^2>250>1
hence b is good.

Engineer1 · Answer

BrentGMATPrepNow ,  Bunuel  - How would I know I have missed a data point and how to select data points to arrive at the correct answer? I never thought of, for instance, plugging in 0.00001. I simply checked for integer and a fraction value (0.5 in my case) and obviously got the wrong answer. Thanks for your response.

mysterymanrog · Answer

never mind made some mistakes =)

bumpbot · Answer

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

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