It is now well-established that most galaxies are host to a supermassive black hole (SMBH) at its galactic center. A few percent of galaxies, collectively known as active galaxies, host an actively accreting black hole. Blazars are a small fraction of active galaxies that are of radio-loud and exhibit relativistic jets where the jet is pointed at a narrow angle along our line of sight. During flaring events, about 10% of the jet power is dissipated from a compact region that cannot be resolved at any energy. As a result, the location of these flaring events is unknown and the distance of a Fermi-detected blazar -ray emission site from a supermassive black hole is a matter of active debate. In this work I present a method for testing whether the GeV emission zone (GEZ) in powerful blazars is produced within the subparsec- scale broad-line region (BLR) or farther out in the parsec-scale molecular torus (MT) environment using the flare falling times as an observable. The location of the GEZ a_ects the source of seed photons that enter the jet and are upscattered to GeV energies via inverse Compton (IC) scattering. Seed photons from the MT are a factor of 100 times less energetic than seed photons from the BLR. This energy difference aspects whether cooling occurs in the Klein-Nishina or Thomson regime. If the GeV emission takes place within the BLR, the inverse Compton (IC) scattering of the BLR ultraviolet (UV) seed photons that produces the -rays takes place at the onset of the Klein-Nishina regime. This causes the electron cooling time to become practically energy-independent and the variation of the gamma-ray emission to be almost achromatic. If, on the other hand, the -ray emission is produced farther out in the parsec-scale MT, the IC scattering of the infrared (IR) MT seed photons that produces the -rays takes place in the Thomson regime, resulting in energy-dependent electron cooling times, manifested as energy dependent cooling times of GeV flares. To demonstrate the viability and application of this method I used a combination of numerical modeling and observational application. In the numerical model I created GeV flares that take place alternately in the BLR and the MT by changing the energy density and source of seed photons. The output of this model demonstrates the predicted energy independence of are falling times in flares originating in the BLR and energy dependence of are falling times in flares originating in the MT. I then apply this diagnostic of locating the GEZ to blazar PKS 1510-089 using four bright gamma-ray flares detected by the Fermi gamma-ray observatory in 2009. In the two cases where the gamma-ray flare was not accompanied by an optical flare, the decay times show an energy-dependence suggesting a location in the MT. For the two GeV flares accompanied by optical flares, we obtained very fast decay times (3 hr) in both low and high energy Fermi bands, indicating energy independence suggesting a possible location in the BLR. We thus conclude that the GEZ is spread over a wide range of locations beyond the BLR.