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a = b + 1 and 5 < ab < 8
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01 Dec 2020, 03:06
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57% (01:30) wrong based on 33 sessions
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\(a = b + 1\) and \(5 < ab < 8\)
Quantity A
Quantity B
\(2a+b^2\)
\(a^2+2b\)
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.
Since we're told \(a = b + 1\), we can replace \(a\) with \(b + 1\) to get: Quantity A: \(2(b + 1)+b^2\) Quantity B: \((b + 1)^2+2b\)
Expand and simplify both quantities: Quantity A: \(b^2+2b+2\) Quantity B: \(b^2+4b+1\)
Subtract \(b^2\) from both quantities: Quantity A: \(2b+2\) Quantity B: \(4b+1\)
Subtract \(2b\) from both quantities: Quantity A: \(2\) Quantity B: \(2b+1\)
Subtract \(1\) from both quantities: Quantity A: \(1\) Quantity B: \(2b\)
Divide both quantities by \(2\): Quantity A: \(0.5\) Quantity B: \(b\)
We're told that 5 < ab < 8, however there are infinitely many values of a and b that satisfy this inequality. For example, it could be the case that a = -2 and b = -3, in which case, Quantity A is greater It could also be the case that a = 3 and b = 2, in which case, Quantity B is greater