Melisa,
As Adam has mentioned, the prerequisites should be met for enrollment at ATP - granted there may be an exemption, but you’d have to contact admin to see if applicable:
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Written tests can be completed at any time; HOWEVER, they are only VALID for 2 years after taking them, so it is important to not take them too early. At ATP if you enroll and start taking them, you will not touch the 2-year timeframe since the program is 7-months long. Like Adam mentioned, you must an endorsement for the following test: PAR, IRA and CAX. This thread posting about taking the AKT breaks down which tests, which ones require endorsements and things to know going into a written test: Preparing for Your Airman Knowledge Test - Frequently Asked Questions - Airline Pilot Life
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Back in June of this year, I believe ATP’s success rate of checkrides was 84%, and it was rising. I’m sure we can get an exact number, but do know ATP is one of the, if not most successful aviation training schools out there. Earlier this month in FLYING Magazine, ATP was ranked #1: Top Flight Schools Revealed - FLYING Magazine
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Here is the actual regulation that will pertain to your son if he attends ATP for flight training, it is listed under 14 CFR Part 61.159 which breaks down the required hours. Most regional airlines will accept new hires at 1,475 since you can use 25 hours of full motion simulator training towards your 1,500.
Please let us know if there is anything else we didn’t answer, welcome to the forum 
Brady