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16 Sep 2014, 01:09
Kudos
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16 Sep 2014, 01:09
Kudos
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Official Solution:
Is \(|x + 1| < 2\)?
This can be rewritten as: is \(-2 < x+1 < 2\)? Simplifying further: is \(-3 < x < 1\)?
(1) \((x-1)^2 < 1\).
This implies \(-\sqrt{1} < x-1 < \sqrt{1}\), which translates to \(0 < x < 2\). Therefore, both YES and NO answers are possible (consider \(x=0.9\) and \(x=1.1\), respectively). Not sufficient.
(2) \(x^2-2 < 0\).
This implies \(-\sqrt{2} < x < \sqrt{2}\). Given that \(\sqrt{2} \approx 1.4\), both YES and NO answers remain possible (using the same examples \(x=0.9\) and \(x=1.1\)). Not sufficient.
(1)+(2) Combining (1) and (2), we deduce that \(0 < x < \sqrt{2}\). Still, both YES and NO answers are possible (as demonstrated by the aforementioned examples). Not sufficient.
Answer: E
Is \(|x + 1| < 2\)?
This can be rewritten as: is \(-2 < x+1 < 2\)? Simplifying further: is \(-3 < x < 1\)?
(1) \((x-1)^2 < 1\).
This implies \(-\sqrt{1} < x-1 < \sqrt{1}\), which translates to \(0 < x < 2\). Therefore, both YES and NO answers are possible (consider \(x=0.9\) and \(x=1.1\), respectively). Not sufficient.
(2) \(x^2-2 < 0\).
This implies \(-\sqrt{2} < x < \sqrt{2}\). Given that \(\sqrt{2} \approx 1.4\), both YES and NO answers remain possible (using the same examples \(x=0.9\) and \(x=1.1\)). Not sufficient.
(1)+(2) Combining (1) and (2), we deduce that \(0 < x < \sqrt{2}\). Still, both YES and NO answers are possible (as demonstrated by the aforementioned examples). Not sufficient.
Answer: E
06 Nov 2017, 10:28
Kudos
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Hi Bunuel, for S1, I considered the following, could you please help me understand what mistake I made? Thank you very much.
(x−1)2<1
x2-2x+1<1
x2-2x<0
x(x-2)<0
x<0
x<2
(x−1)2<1
x2-2x+1<1
x2-2x<0
x(x-2)<0
x<0
x<2
