Always note the values in the quantities to inform your approach to any Quantitative Comparison. In this case, although we are presented a quadratic, it may actually make sense to attempt to manipulate the equation to find x + 1 since that is the value of Quantity A.

So, add 40 to each side of the equation to find that x^2 + x = 40. Then, factor the left hand side of the equation to find that x(x+1) = 40. Now, just plug 5 in as x to determine the relationship between the quantities.

If x = 5, then x(x + 1) = 5 x 6 = 30 which is < 40. Then, testing if x = 6, we discover that 6 x 7 = 42. So, therefore 5 < x < 6.

Now for the negative solution just flip the x and x - 1.

So, if x = -6, then x(x + 1) = -6 x -5 = 30 which again is < 40. Then, testing if x = -7, we discover again that -7 x - 6 = 42. So, therefore -7 < x < -6.

Now apply the ranges to test the possibilities for Quantity A. If x > 5 then |x + 1| > 5. If x < -6 then |x + 1| > 5.

In both cases Quantity A is greater, so select Choice A.