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27 Dec 2019, 12:05
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Difficulty:
15%
(low)
Question Stats:
75% (00:52) correct
25%
(00:42)
wrong
based on 68
sessions
History
Date
Time
Result
Not Attempted Yet
Which of the following describe all values of m for which m^4 > 16 ?
A. m > 4
B. m > 2
C. -2 < m < 2
D. m > 2 or m < -2
E. m > 4 or m < -4
A. m > 4
B. m > 2
C. -2 < m < 2
D. m > 2 or m < -2
E. m > 4 or m < -4
27 Dec 2019, 12:14
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\(m^{4} = |m|^{4} >16\)
\(=> |m| >2\)
=> \(m>2\) or \(m<-2\)
\(=> |m| >2\)
=> \(m>2\) or \(m<-2\)
27 Dec 2019, 16:11
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Nali2020
Thank you for posting the question, Nali2020. This question can be used to illustrate how to use the answer choices and test their validity instead of rushing to get an answer and blundering into a trap. Looking at (B), of course, since \(2^4 = 16\), anything greater than 2 will create a valid inequality. However, I imagine a few test-takers would be quick at the trigger and choose (B) without considering the negative end of the spectrum. Since three of the five answer choices do, though, that should serve as a tipoff (if the even power had not already done so). (C) represents another decent trap answer. The crucial points -2 and 2 are there, but the inequalities are messed up. We already know, for example, that m should be greater than 2 on the positive end. Still, testing a number such as 0 clearly breaks down the inequality in the question. Thus, (C) is out. A quick look at (D) and a trial with a number such as -3 is easy enough, maybe adding 5 seconds more:
\((-3)^4 = 81\)
But those are 5 seconds well spent.
Thank you again for sharing.
- Andrew
