Given that x ≠5, is x>{1/(x-5)^2}

[BTGmoderatorDC]

Given that x ≠ 5, is x>{1/(x-5)^2}

Statement #1: x > 0

Statement #2: x > 10

OA B

Source: Magoosh

[Jay@ManhattanReview]

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

Statement #1: x > 0

Statement #2: x > 10

OA B

Source: Magoosh

Given: x ≠ 5

Question: Is x > {1/(x - 5)^2}?

Let's take each statement one by one.

(1) x > 0

Case 1: Say x = 11

Thus, x > {1/(x - 5)^2} = 11 ? {1/(11 - 5)^2} => 11 > 1/36. The answer is Yes.

Case 2: Say x = 1/100

Thus, x > {1/(x - 5)^2} = 1/100 ? {1/(1/100 - 5)^2} => 1/100 > A very big number. The answer is No.

No unique answer. Insufficient.

(2) x > 10

We have seen that for x = 11, the answer is yes. As we increase the value of x, the value of 1/(x - 5)^2 will decrease further. Thus, the answer would be Yes.

The correct answer: B

Hope this helps!

-Jay
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[fskilnik@GMATH]

Given that x ≠ 5, is x>{1/(x-5)^2}

Statement #1: x > 0

Statement #2: x > 10
Source: Magoosh

$$x\,\,\mathop > \limits^? \,\,\frac{1}{{{{\left( {x - 5} \right)}^2}}}\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,x{{\left( {x - 5} \right)}^2}\,\,\mathop > \limits^? \,\,1\,\,\,{\text{with}}\,\,{\text{x}} \ne {\text{5}}\,\,}$$
$$\left( 1 \right)\,\,\,x > 0\left\{ \matrix{
\,{\rm{Take}}\,\,{\rm{x = 1}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,{\rm{x = 5 + }}{1 \over {10}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\left[ {5.1 \cdot {1 \over {100}} < 1} \right] \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\,x > 10\,\,\, \Rightarrow \,\,\,{\left( {x - 5} \right)^2} > 25\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

[Kyron GMAT]

The above image is a screen grab from my video solution to this problem. The full video is free at https://youtu.be/jSx4fXcdPEc $$$$

[Brent@GMATPrepNow]

Given that x ≠ 5, is x>{1/(x-5)^2}

Statement #1: x > 0

Statement #2: x > 10

OA B

Source: Magoosh

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

Cheers,
Brent