We're told that a is positive, and zero isn't positive.

Brent,

Since a+6:b+6 is a represented in a ratio, couldn't b be anything?

For example: a+6:b+6 = 5:6 or a+6:b+6 = 10:12

So this would mean that a:b = 4:6 or a:b = 2:3

We can manipulate the ratio a:b to become anything we want at this point.

a:b = 2/3 : 1
a:b = 1/6 : 1/4
a:b = 20 : 30
.
.
.


This would give D. Have I thought about this problem incorrectly?

I think yes.

if you see above the exdplanation by Brent you spot immediately the solution

The gist of the problem is not the ratio itself but to ascertain if B added to some other number is > 1 or < 1

Regardless the ratio

Regards

I like the way you're approaching this question. You're using a lot of number sense, which is a great skill to have for QC questions.
Notice that, for for your example, we get a = 4 and b = 6
In this case, quantity A is greater than quantity B (since 6 > 1)

The key here is that a and b must be positive.
If you continue with your line of reasoning, you'll find it quite difficult to find a positive value of b that's less than quantity B (1)

Thanks Carcass and Brent.

I just realized that manipulating the ratio the way I did would not satisfy the ratio a+6:b+6 = 5:6

So a:b = 2:3 we would get a+6:b+6 = 8:9 which does not equal the ratio 5:6.

The only way to generalize the ratio a:b for all a and b is in the explanation Brent gave

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