Alzheimer’s Disease (AD) is the most expensive and currently incurable disease that affects a large number of the elderly globally. One in five Medicare dollars is spent on AD-related tests and treatments. Accurate AD diagnosis is critical but often involves invasive and expensive tests that include brain scans and spinal taps. Recommending these tests for only patients who are likely to develop the disease will save families of cognitively normal individuals and hospitals from unnecessary expenditures. Moreover, many of the subjects chosen for clinical trials for AD therapies never develop any cognitive impairment and prove not to be ideal candidates for those trials. It is thereby critical to find inexpensive ways to first identify individuals who are likely to develop cognitive impairment and focus attention on them for in-depth testing, diagnosing, and clinical trial participation. Research shows that AD is a slowly progressing disease. This slow progression allows for early detection and treatment, but more importantly, gives the opportunity to predict the likelihood of disease development from early indications of memory lapses. Neuropsychological tests have been shown to be effective in identifying cognitive impairment. Relying exclusively on a set of longitudinal neuropsychological test data available from the ADNI database, this paper has developed Recurrent Neural Network (RNN) models to predict future neuropsychological test results and Multi-Level Perceptron (MLP) models to diagnose the future cognitive states of individuals based on those predicted results. The RNNs use sequence prediction techniques to predict test scores for two to four years in the future. The predicted scores and predictions of cognitive states based on them showed a high level of accuracy for a group of test subjects, when compared with their known future cognitive assessments conducted by ADNI. This shows that a battery of neuropsychological tests can be used to track the cognitive states of people above a certain age and identify those who are likely to develop cognitive impairment in the future. This ability to triage individuals into those who are likely to remain normal and those who will develop cognitive impairment in the future, advances the quest to find appropriate candidates for invasive tests like spinal taps for disease identification, and the ability to identify suitable candidates for clinical trials.