y is a positive integer. Quantity A y2 + 2 Quantity B 3y - 1
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Quantity A is greater.
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Quantity B is greater.
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The two quantities are equal.
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The relationship cannot be determined from the information given.
Reveal answer
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A
Correct answer
Explanation
Compare y^2 + 2 and 3y - 1. For y=1, A=3, B=2 (A>B). For y=2, A=6, B=5 (A>B). For y=3, A=11, B=8 (A>B). Since y^2 - 3y + 3 = (y - 1.5)^2 + 0.75, which is always positive, y^2 + 2 is always greater than 3y - 1.
AI explanation
Subtracting 3y from both sides and adding 1 gives y^2 - 3y + 3. The discriminant of this quadratic is (-3)^2 - 4(1)(3), which equals 9 - 12 or -3. Since the discriminant is negative and the leading coefficient is positive, y^2 - 3y + 3 is always positive for any real value of y. Therefore, y^2 + 2 is always greater than 3y - 1.