I don't see how you could know X1 and X2 are correlated from the formula alone. So I don't see how A could be correct.

Answer "A" could be correct.The mathematics behind OLS allow us to know if a correlation exists between the two variables or if one of the variables (X2 in this case) has a non-zero coefficient. If X1 and X2 are uncorrelated in this model the parameter estimate of X1 will be unchanged by the addition of X2 to the model (assuming that X1 and X2 parameters are nonzero). The parameter estimates of X1 and X2 would change when the other is added to the model only if there is some "shared" information between them pertaining to Y.

Let:

1) y= bo + b1x1

2) y= Bo + B1x1 + B2x2

b1 = B1 + B2d1

d1 represents the slope from regressing x2 on x1.

For b1 to equal B1, the correlation between x1 and x2 must be zero (since they're not constants, the variances/sds will be strictly positive), or B2 must actually equal zero. We can see various ways that b1 can approximate B1.

I more or less summarized this example from Wooldridge,

*Introductory Econometrics: A Modern Approach*, since he did a pretty good job with it. So, you can do a bit of thinking with the output and the theory and make reasonable conclusions regarding the correlation between x1 and x2 or Xi and all other X's (if the model had more than 2 X variables).

I think B has problems that have come up before: you can purely state that a 1 unit change in x1 changes Y by a greater magnitude than a 1 unit change in x2 does, but it gets hairy to say anything different from a plain statement like this when X1 and X2 are measured on different scales. A 1 inch increase in height may decrease life expectancy by 5 years, while a 1 pound increase in yearly meat consumption my decrease life expectancy by 2 years, but who's to say a 1 inch change is equivalent or as meaningful as a 1 pound change in meat consumption. The most we can do with that, I think, it speak strictly in terms of magnitudes and not importance, and choice B seems to stay close enough to the safe answer of just magnitudes.

Choice A is possible, too, I think, based on the explanation I mentioned from Wooldridge. I think I might be missing something or the question wasn't written as well as it could have been.