Have a oil leak around engine

GM states one quart within 2,000 miles is acceptable with properly maintained engines. There are different aspects to this question and it deserves further testing. What type of oil do you use? What are the oil change intervals? Is the truck normally driven loaded or empty? Is the truck subject to a lot of stop and go driving or highway? The first thing is to change the oil and filter, drive the vehicle for 600 miles and verify the current oil level. If the oil is not leaking externally and is not mixing with the coolant. The oil is burned inside the exhaust system. Worn out PCV valve, damaged thermostat, Leaking fuel injector/s, worn valve guides or broken piston oil wiper ring could be to blame but further testing is needed.

It can easily burn that much in a 100 miles without seeing any smoke.
If you check the spark plugs you may find evidence.
It can also leak while the engine is running and not when it is off. Most Northstar engines leak to some degree.

One quart per month is a bit more than I'd expect but you didn't mention how many miles you drive during that month.If you live where the ambient temps are very warm, it may help to use a good synthetic. Synthetic oils do not burn off or break down chemically as fast as conventional oils do. I'd use a 20w40 grade.
Depending on the miles you've driven you shouldn't have excessive ring wear but the valve stem seals may have dried out and cracked. If the usage remains constant and there is no smoking etc, you could either leave it alone or have new seals installed.
Average driving is approximately 1,000 miles per month so when figuring consumption, use that as a baseline. One quart per 1,000 miles in very hot conditions is a bit high....I'd expect to see 1/2 qt or slightly less. One odd thing though is that generally, especially in an engine that holds six quarts to begin with, at five quarts, the engine should not feel any different!!!
Also.....you use miles to determine oil change intervals. Oil is best changed at between 3K and 4K miles. Only way you use the 3month method is if you don't use it much. (you can run most good synthetics longer than that)

Engine needs an oil treatment. Rings could be losing compression. Rislone.

My 1993 voyager is like that. It may burn some , it definitely leaks some , and it could be just sending some through the PCV valve. Oil leaks and burning oil causes pollution . If you can fix it with a new seal or a valve cover gasket it is easier than constantly checking your oil. Temperature, trailering, speed, outdoor temperature, and engine RPM all can be factors if you are losing oil. If your engine is a quart down, the engine oil consumption rate doubles or triples. In other words the lower the oil level the faster it disappears. High mile cars will drive for years as long as you add oil when it is needed (keep the oil level between the marks). Fix any obvious leaks. Then determine your oil change interval (3000 miles, 4000 miles, 5000 miles). I change between 4000 and 5000 miles. If i am a quart low at 3500 I add a quart. If I am a quart low at 4500 miles I just change the oil in the car. A good practice is to carry a quart of oil in your vehicle just in case you need it. It is far cheaper to add a quart when needed than to go to the dealer once to maybe fix a problem that they may not be able to find or fix. Older engines (even some newer ones) just use oil , especially in hotter climates. Fix the obvious and carry a quart.

if it is not leaking then it is being burned by the engine, how many miles go by before you need to add oil?, if u are adding more than one quart every 1000 miles u have piston reing problems and or valve guide seal leaks. U won't see any smoke in most cases unless you are really going through the oil, like 1 quart every 300 miles.

Now I am really depressed. We thought we have a change from driving Honda and Toyota so we decided to buy a new 2009 Tribeca. My first oil change for this car was 1800 miles, after breaking in. I replaced it with 7 qts of Mobile 1 Full Synthetic. Currently, the car has 8900 miles, that is 7100 driven; unfornately, I just filled 3 qts of new Mobile 1. Luckily, I check!!! Is this normal for Tribeca? If so, this is the worst investment of a lifetime. I won't ever buy Subaru again or recommend to anyone!!!

A quart /1000 miles is on the high side for that mileage- something abnormal is causing it.
1) Ensure any motor oil leaks are fixed to ensure they are not contributing to the oil loss.
2) Observe if any blue smoke from exhaust on downhill coast/deceleration - if present it indicates worn valve stem oil seals (these can be replaced relatively cheaply).
3) If blue smoke from exhaust on acceleration the piston rings may be worn- (costly repair).

your pvc valve not working.or you have leaking valve seals or worn valve guides wornrings .and your oil return holes get stop up oil.

Every manufacturer has a guideline.  But a quart every 1,000 miles seems higher then necessary.  Try the easy steps first. 1.  Check the PCV valve if clogged will caused pressure in crankcase and oil burning. 2. Remove spark plugs and perform visual inspection.  IF electrode is covered in gook(technical terms, sorry), then oil is leaking into that cylinder.  Most likely cause would be faulty valve stem seals. 3. Worse case scenario, engine oil rings are leaking.  If all else is good.  Perform compression test of each cylinder recording measurement, then add two small squirt of engine oil into each cylinder as you perform a second round, complete both dry then wet compression test on each cylinder before proceeding.  IF any cylinder shows a more significant increase in compression then it would indicate that cylinder's oil rings are faulty.  This is a major repair.  Keep me posted