We can solve this question using matching operations (my favorite Quantitative Comparison strategy)

Given:
Quantity A: \(2a+b^2\)
Quantity B: \(a^2+2b\)

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

Answer: D

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