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If x^3 < 16x, which of the following CANNOT be true?
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06 Jan 2022, 06:30
06 Jan 2022, 06:30
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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?
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11 Jan 2022, 06:44
11 Jan 2022, 06:44
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Let's first simplify the expression:
x^3 < 16x
x^3 - 16x <0
x(x-4)(x+4)<0
For the expression above hold true, x<-5 (i.e. -5, -10) or 4>x>0 (i.e. 1,2) -- one can easily visualize this using the number line
Now that we know for which values the expression is true, let's eliminate the alternatives that CAN be true:
(A) |x| > 4 -> true for x=-5
(B) x > −4 -> true for x=1
(C) x < −4 -> true for x=-5
(D) x > 4 -> not true for any of our values
(E) x < 4 -> true for x=1
IMO D
Please give kudos if you like the explanation
x^3 < 16x
x^3 - 16x <0
x(x-4)(x+4)<0
For the expression above hold true, x<-5 (i.e. -5, -10) or 4>x>0 (i.e. 1,2) -- one can easily visualize this using the number line
Now that we know for which values the expression is true, let's eliminate the alternatives that CAN be true:
(A) |x| > 4 -> true for x=-5
(B) x > −4 -> true for x=1
(C) x < −4 -> true for x=-5
(D) x > 4 -> not true for any of our values
(E) x < 4 -> true for x=1
IMO D
Please give kudos if you like the explanation
General Discussion
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Re: If x^3 < 16x, which of the following CANNOT be true?
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06 Jan 2022, 07:05
06 Jan 2022, 07:05
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Bunuel 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.
