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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If x^3 < 16x, which of the following CANNOT be true? (A) |x| > 4 (B)
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04 Apr 2021, 22:47
04 Apr 2021, 22:47
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Question Stats:
57% (01:42) correct
42% (02:01) wrong based on 14 sessions
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If \(x^3 < 16x\), which of the following CANNOT be true?
(A) \(|x| > 4\)
(B) \(x > −4\)
(C) \(x < −4\)
(D) \(x > 4\)
(E) \(x < 4\)
(A) \(|x| > 4\)
(B) \(x > −4\)
(C) \(x < −4\)
(D) \(x > 4\)
(E) \(x < 4\)
If x^3 < 16x, which of the following CANNOT be true? (A) |x| > 4 (B)
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05 Apr 2021, 23:59
05 Apr 2021, 23:59
2
\(x^3 < 16x\)
\(x (x^2 - 16) < 0\)
Turning this equation into identity form,
\(x (x+4) (x-4) < 0\)
Finding the range of x on the number line,
So, x < -4, or 0 < x < 4
Every other option except D can be true in either of these cases. x cannot be greater than 4.
Hence, D is the correct answer.
\(x (x^2 - 16) < 0\)
Turning this equation into identity form,
\(x (x+4) (x-4) < 0\)
Finding the range of x on the number line,
So, x < -4, or 0 < x < 4
Every other option except D can be true in either of these cases. x cannot be greater than 4.
Hence, D is the correct answer.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x^3 < 16x, which of the following CANNOT be true? (A) |x| > 4 (B)
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15 Jan 2022, 11:48
15 Jan 2022, 11:48
GeminiHeat wrote:
If \(x^3 < 16x\), which of the following CANNOT be true?
(A) \(|x| > 4\)
(B) \(x > −4\)
(C) \(x < −4\)
(D) \(x > 4\)
(E) \(x < 4\)
(A) \(|x| > 4\)
(B) \(x > −4\)
(C) \(x < −4\)
(D) \(x > 4\)
(E) \(x < 4\)
Testing values is a quick and effective approach...
If x³ < 16x, then it COULD be the case that x = -5, since (-5)³ = -125, 16(-5) = -80, and -125 < -80
Since x can equal -5, we can eliminate answer choices A, C and E, since they all state that x CAN equal -5
Similarly, x³ < 16x, then it COULD be the case that x = 1, since 1³ = 1, 16(1) = 16, and 1 < 16
Since x can equal 1, we can eliminate answer choice B since it states that x CAN equal 1
By the process of elimination, the correct answer is D
In other words, x CANNOT be greater than 4.
