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04 Sep 2020, 20:00
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D
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Difficulty:
85%
(hard)
Question Stats:
50% (02:09) correct
50%
(02:00)
wrong
based on 565
sessions
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If \(x^4 > 50\), then which of the following must be true?
A. \(|x| > 3\)
B. \(x > 2.5\)
C. \(x < 2.5\)
D. \(\frac{1}{|x|} < 0.4\)
E. \(\frac{1}{|x| }> 0.4\)
M37-88
A. \(|x| > 3\)
B. \(x > 2.5\)
C. \(x < 2.5\)
D. \(\frac{1}{|x|} < 0.4\)
E. \(\frac{1}{|x| }> 0.4\)
|
M37-88
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03 Dec 2021, 07:08
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Official Solution:
If \(x^4 > 50\), then which of the following must be true?
A. \(|x| > 3\)
B. \(x > 2.5\)
C. \(x < 2.5\)
D. \(\frac{1}{|x|} < 0.4\)
E. \(\frac{1}{|x|} > 0.4\)
\(x^4 > 50\) means that \(x < -\sqrt[4]{50}\) or \(x > \sqrt[4]{50}\).
Check each option:
A. \(|x| > 3\). Take to the fourth power: \(x^4 > 81\). This one is not necessarily true. For example, consider \(x^4=60\).
B. \(x > 2.5\). This one is not not necessarily true. For example, consider \(x=-10\).
C. \(x < 2.5\). This one is not necessarily true. For example, consider \(x=10\).
D. \(\frac{1}{|x|} < 0.4\). Simplify: \(|x| > \frac{5}{2}\). Take to the fourth power: \(x^4 > 40\) (\((\frac{5}{2})^4=\frac{625}{16}\approx 40\)). Since given that \(x^4\) is greater than 50, then it's obviously greater than 40. This one is true.
E. \(\frac{1}{|x|} > 0.4\). Simplify: \(|x| < \frac{5}{2}\). Take to the fourth power: \(x^4 < 40\). This one is NOT true.
Answer: D
If \(x^4 > 50\), then which of the following must be true?
A. \(|x| > 3\)
B. \(x > 2.5\)
C. \(x < 2.5\)
D. \(\frac{1}{|x|} < 0.4\)
E. \(\frac{1}{|x|} > 0.4\)
\(x^4 > 50\) means that \(x < -\sqrt[4]{50}\) or \(x > \sqrt[4]{50}\).
Check each option:
A. \(|x| > 3\). Take to the fourth power: \(x^4 > 81\). This one is not necessarily true. For example, consider \(x^4=60\).
B. \(x > 2.5\). This one is not not necessarily true. For example, consider \(x=-10\).
C. \(x < 2.5\). This one is not necessarily true. For example, consider \(x=10\).
D. \(\frac{1}{|x|} < 0.4\). Simplify: \(|x| > \frac{5}{2}\). Take to the fourth power: \(x^4 > 40\) (\((\frac{5}{2})^4=\frac{625}{16}\approx 40\)). Since given that \(x^4\) is greater than 50, then it's obviously greater than 40. This one is true.
E. \(\frac{1}{|x|} > 0.4\). Simplify: \(|x| < \frac{5}{2}\). Take to the fourth power: \(x^4 < 40\). This one is NOT true.
Answer: D
General Discussion
04 Sep 2020, 20:27
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Explanation:
x^4 > 50
Solving above Eqn we get; x =+/- 2.6591.
Means X value lies between -2.6591 to 2.6591
-2.6591 < x < 2.6591
Now checking all options.
A. |x|>3
Wrong as value is less than 3
B. x>2.5
x has negative value too . Incorrect
C. x<2.5
x has greater value than 2.5 too . Incorrect
D. 1/|x| < 0.4
1/|x| will be 0.376 which is less than 0.4 . Correct
IMO-D
Posted from my mobile device
x^4 > 50
Solving above Eqn we get; x =+/- 2.6591.
Means X value lies between -2.6591 to 2.6591
-2.6591 < x < 2.6591
Now checking all options.
A. |x|>3
Wrong as value is less than 3
B. x>2.5
x has negative value too . Incorrect
C. x<2.5
x has greater value than 2.5 too . Incorrect
D. 1/|x| < 0.4
1/|x| will be 0.376 which is less than 0.4 . Correct
IMO-D
Posted from my mobile device
