I believe 60-120 is actually considered normal for a non-diabetic.
As a type 1 lifelong diabetic myself, I try to stay in the 80-120 range because that is where I am comfortable (that is usually what they recommend for kids), but I know my doc thinks it is safe for me to fall as low as 60, as this is fine for non-diabetics.
Personally, in the 60 range I get like a lunatic. By 50 I am on the verge of unconciousness, and I will begin having convulsions between 40 and 30.
My other diabetic friends tell me they have no trouble at 60. Maybe it is personal.
The mere fact that you, as a nondiabetic, are concerned enough with your blood sugar to have a glucometer tells me there is something going on. I would report your low blood sugar incident to your doc, especially if this happens frequently. You may indeed have hypoglycemia.
By the way, to treat your low-blood sugar, it is not recommended you have sweets. For a type 1 diabetic it isn't a big deal, but for someone whose body produces insulin (such as a hypoglycemic or a type 2 diabetic), if you eat sweets, when your blood sugar starts shooting back up, your body is likely to over react and then overproduce more insulin, causing another low shortly thereafter.
When you get low like you did today, try eating a bit of complex carbohydrate (such as a couple of crackers or a peice of toast) and following that with a glass of milk or other protein. As an alternative have a half a cheese or meat sandwich. Be patient as you wait for your blood sugar to rise. Eating more wont necessarily bring it up faster, it will just give your body more to overreact about later.
Eating small bits throughout the day will also be a helpful preventative measure if you are indeed likely to get low blood sugar.
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