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x^2+3 or 3x-2
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22 Mar 2021, 10:04
22 Mar 2021, 10:04
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Question Stats:
84% (01:15) correct
15% (00:50) wrong based on 45 sessions
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Quantity A |
Quantity B |
\(x^2+3\) |
\(3x-2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: x^2+3 or 3x-2
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22 Mar 2021, 19:14
22 Mar 2021, 19:14
1
Qt A
\(x^2\) will always be greater than or equal to 0
So if we take x=0
Qt A = 3
Qt B will be -2
So in every case
Qt A > Qt B
Answer A
\(x^2\) will always be greater than or equal to 0
So if we take x=0
Qt A = 3
Qt B will be -2
So in every case
Qt A > Qt B
Answer A
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x^2+3 or 3x-2
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23 Mar 2021, 08:31
23 Mar 2021, 08:31
Carcass wrote:
Quantity A |
Quantity B |
\(x^2+3\) |
\(3x-2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Col. A: \(x^2 + 3\)
Col. B: \(3x - 2\)
Subtracting \(3x - 2\) from both sides;
Col. A: \(x^2 - 3x + 5\)
Col. B: \(0\)
Let's find the vertex of this up-right Parabola:
x-coordinate of the vertex = \(\frac{-b}{2a} = \frac{-(-3)}{(2)(1)} = \frac{3}{2}\)
y-coordinate of the vertex = \((\frac{3}{2})^2 - (3)(\frac{3}{2}) + 5 = \frac{11}{4} = 2.75\)
This means the \(y\) value for this Parabola can never be equal to or less than \(0\)
Col. A: A number greater than equal to \(2.75\) for any value of \(x\)
Col. B: \(0\)
Hence, option A
