Given:\(\frac{p-q}{p+q} = \frac{2}{3}\)
Multiply both sides by (p+q) to get: \(p-q = (\frac{2}{3})(p+q)\)
Multiply both sides by 3 to get: \(3(p-q) = (2)(p+q)\)
Expand both sides to get: \(3p-3q = 2p+2q\)
Subtract 2p from both sides to get: \(p-3q = 2q\)
Add 3q to both sides to get: \(p = 5q\)

Now take given quantities and replace p with 5q to get:
Quantity A: 5q + q
Quantity B: 5

Simplify:
Quantity A: 6q
Quantity B: 5

Let's TEST some values of q

CASE i: If q = 1/6, then we get:
Quantity A: 6(1/6) = 1
Quantity B: 5
In this case, Quantity B is greater

CASE ii: If q = 1, then we get:
Quantity A: 6(1) = 6
Quantity B: 5
In this case, Quantity A is greater

Answer: D

RELATED VIDEO FROM OUR COURSE