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07 Sep 2022, 05:19
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (02:19) correct
41%
(02:24)
wrong
based on 109
sessions
History
Date
Time
Result
Not Attempted Yet
Is |x + 1| < 2 ?
(1) (x - 1)^2 < 1
(2) x^2 - 2 < 0
(1) (x - 1)^2 < 1
(2) x^2 - 2 < 0
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07 Sep 2022, 05:57
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Question
Is |x + 1| < 2
We know that if |x| < m
-m < x < m
Using the same concept we can find the range of x
-2 < x+1 < 2
Subtracting 1 on both sides of the equation
-3 < x < 1
So the question translates to => Does -3 < x < 1 ?
Statement 1
\((x-1)^2 < 1\)
Taking square root on both sides
|(x-1)| < 1
0 < x < 2
Does -3 < x < 1 ? - Yes as well as No ! Hence this statement is not sufficient. Hence we can eliminate option A and D
Statement 2
\((x)^2 - 2 < 0\)
Adding 2 on both sides and taking square root on both sides
\(|x| < \sqrt{2}\)
-\(\sqrt{2}\) < x < \(\sqrt{2}\)
Does -3 < x < 1 ? - Yes as well as No !
Eliminate B
Combined
0 < x < \(\sqrt{2}\)
Does -3 < x < 1 ? - Yes as well as No !
Option E
Is |x + 1| < 2
We know that if |x| < m
-m < x < m
Using the same concept we can find the range of x
-2 < x+1 < 2
Subtracting 1 on both sides of the equation
-3 < x < 1
So the question translates to => Does -3 < x < 1 ?
Statement 1
\((x-1)^2 < 1\)
Taking square root on both sides
|(x-1)| < 1
0 < x < 2
Does -3 < x < 1 ? - Yes as well as No ! Hence this statement is not sufficient. Hence we can eliminate option A and D
Statement 2
\((x)^2 - 2 < 0\)
Adding 2 on both sides and taking square root on both sides
\(|x| < \sqrt{2}\)
-\(\sqrt{2}\) < x < \(\sqrt{2}\)
Does -3 < x < 1 ? - Yes as well as No !
Eliminate B
Combined
0 < x < \(\sqrt{2}\)
Does -3 < x < 1 ? - Yes as well as No !
Option E
27 Apr 2023, 02:17
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Official Solution:
Is \(|x + 1| < 2\)?
Eliminate the absolute value: Is \(-2 < x + 1 < 2\)?
Subtract 1 from all parts: Is \(-3 < x < 1\)?
(1) \((x - 1)^2 < 1\)
Taking the square root results in \(|x - 1| < 1\).
Eliminate the absolute value: \(-1 < x - 1 < 1\)
Add 1 to all parts: \(0 < x < 2\)
Since we can have both a YES and a NO answer to the question whether \(-3 < x < 1\), this statement is not sufficient.
(2) \(x^2 - 2 < 0\)
Rearrange: \(x^2 < 2\)
Taking the square root results in \(|x| < \sqrt{2}\).
Eliminate the absolute value: \(-\sqrt{2} < x < \sqrt{2}\)
\(\sqrt{2} \approx 1.4\), so the inequality implies \(-1.4 < x < 1.4\)
Since we can have both a YES and a NO answer to the question whether \(-3 < x < 1\), this statement is not sufficient.
(1)+(2) Combining the constraints \(0 < x < 2\) and \(-1.4 < x < 1.4\) results in the final range of \(0 < x < 1.4\). Yet again, we can have both a YES and a NO answer to the question whether \(-3 < x < 1\). Thus, the combined statements are not sufficient.
Answer: E
Is \(|x + 1| < 2\)?
Eliminate the absolute value: Is \(-2 < x + 1 < 2\)?
Subtract 1 from all parts: Is \(-3 < x < 1\)?
(1) \((x - 1)^2 < 1\)
Taking the square root results in \(|x - 1| < 1\).
Eliminate the absolute value: \(-1 < x - 1 < 1\)
Add 1 to all parts: \(0 < x < 2\)
Since we can have both a YES and a NO answer to the question whether \(-3 < x < 1\), this statement is not sufficient.
(2) \(x^2 - 2 < 0\)
Rearrange: \(x^2 < 2\)
Taking the square root results in \(|x| < \sqrt{2}\).
Eliminate the absolute value: \(-\sqrt{2} < x < \sqrt{2}\)
\(\sqrt{2} \approx 1.4\), so the inequality implies \(-1.4 < x < 1.4\)
Since we can have both a YES and a NO answer to the question whether \(-3 < x < 1\), this statement is not sufficient.
(1)+(2) Combining the constraints \(0 < x < 2\) and \(-1.4 < x < 1.4\) results in the final range of \(0 < x < 1.4\). Yet again, we can have both a YES and a NO answer to the question whether \(-3 < x < 1\). Thus, the combined statements are not sufficient.
Answer: E
