A 52-year-old man from rural Maharashtra presents with a 3-week history of persistent cough and low-grade fever. Chest X-ray shows a cavitary lesion in the right upper lobe. Sputum smear microscopy is positive for acid-fast bacilli (AFB). A rapid molecular test (GeneXpert MTB/RIF) is ordered. The test has a reported sensitivity of 98% and specificity of 99% in the hospital laboratory. Given the high pretest probability of tuberculosis in this clinical scenario (estimated at 85%), what is the approximate positive predictive value (PPV) of a positive GeneXpert result in this patient?