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02 Oct 2024, 12:23
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
0% (00:00) correct
100% (01:40) wrong based on 2 sessions
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x > 0 and x ≠ 1.
Quantity A
\((2x^{-4})(3x^2)\)
Quantity B
\(\frac{24x}{4x^2}\)
Quantity A
\((2x^{-4})(3x^2)\)
Quantity B
\(\frac{24x}{4x^2}\)
04 Mar 2025, 12:23
Kudos
Bookmarks
OE
The two quantities can be simplifed as follows.
Quantity A: \((2x^{-4})(3x^2) = \frac{6}{x^2}\)
Quantity B: \(\frac{24x}{4x^2} =\frac{6}{x}\)
So comparing Quantity A with Quantity B is the same as comparing \(\frac{6}{x^2}\) with \(\frac{6}{x.}\)
Since you are given that x > 0 and x ≠ 1, and the quantities to be compared involve fractions and exponents, it is reasonable to consider two cases: \(0 < x < 1\) and \(x > 1.\)
Case 1: 0 < x < 1. If x is a number that satisfes 0 < x < 1, then \(x^2 < x\). Therefore \(\frac{6}{x^2} > \frac{6}{x}\), and Quantity A is greater than Quantity B.
Case 2: x > 1. If x is a number that satisfes x > 1, then x2 > x. Therefore \(\frac{6}{x^2} <\frac{6}{x}\), and Quantity B is greater than Quantity A.
In one case Quantity A is greater, and in the other case Quantity B is greater. Thus the correct answer is Choice D.
The two quantities can be simplifed as follows.
Quantity A: \((2x^{-4})(3x^2) = \frac{6}{x^2}\)
Quantity B: \(\frac{24x}{4x^2} =\frac{6}{x}\)
So comparing Quantity A with Quantity B is the same as comparing \(\frac{6}{x^2}\) with \(\frac{6}{x.}\)
Since you are given that x > 0 and x ≠ 1, and the quantities to be compared involve fractions and exponents, it is reasonable to consider two cases: \(0 < x < 1\) and \(x > 1.\)
Case 1: 0 < x < 1. If x is a number that satisfes 0 < x < 1, then \(x^2 < x\). Therefore \(\frac{6}{x^2} > \frac{6}{x}\), and Quantity A is greater than Quantity B.
Case 2: x > 1. If x is a number that satisfes x > 1, then x2 > x. Therefore \(\frac{6}{x^2} <\frac{6}{x}\), and Quantity B is greater than Quantity A.
In one case Quantity A is greater, and in the other case Quantity B is greater. Thus the correct answer is Choice D.
