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S99-06

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S99-06  [#permalink]

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New post 16 Sep 2014, 01:53
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

36% (01:19) correct 64% (01:57) wrong based on 85 sessions

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Re S99-06  [#permalink]

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New post 16 Sep 2014, 01:53
Official Solution:


Rephrase the question by expanding the left side of the inequality:

Is \(x^2 - 4x + 4 \gt x^2\)?

Is \(-4x + 4 \gt 0\)?

Is \(4 \gt 4x\)?

Is \(1 \gt x\)?

Statement 1: INSUFFICIENT. The values of \(x\) for which \(x^2 \gt x\) are either negative or greater than 1. (Test numbers to prove this.) However, we do not know whether \(x\) is less than or greater than 1.

Statement 2: INSUFFICIENT. The expression \(\frac{1}{x}\) is positive when \(x\) itself is positive. However, again we do not know whether \(x\) is less than or greater than 1.

Statements 1 & 2 together: SUFFICIENT. Combining the two conditions, we see that \(x\) must be greater than 1. This provides a definitive "No" answer to the given question, and thus we have sufficiency.


Answer: C
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Re: S99-06  [#permalink]

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New post 13 May 2017, 10:28
Looking at the second condition of 1/x >1. it is imperative that x<1 for all x>0, So, I thought condition 2 will be sufficient....Dunno whether I am right? :roll: :roll: :roll:
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Re: S99-06  [#permalink]

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New post 13 May 2017, 10:54
amrit3982 wrote:
Looking at the second condition of 1/x >1. it is imperative that x<1 for all x>0, So, I thought condition 2 will be sufficient....Dunno whether I am right? :roll: :roll: :roll:


The question asks whether x < 1, while 1/x > 0 means that x > 0. So, the second statement is not sufficient: if x = 1/2, then the answer will be YES but if x = 2, then the answer will be NO.
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Re: S99-06 &nbs [#permalink] 13 May 2017, 10:54
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