Mock Exam Afternoon Query (Quant Methods)?

Q31 of The Afternoon Mock Exam for Dec 11 candidates, makes a strange claim about estimator consistency increasing with increasing sample size. I’m not allowed to quote the question without violating CFA rules but does anyone else find the explanation of why B is correct to be unsatisfactory? Surely an estimator is either consistent or it is not, there is no measure of consistency.

As n increases, the bias in your sample decreases. Hypothetically, the bias in your sample goes to 0 as n approaches infinity. Therefore it becomes consistent as n increases because distributions of the estimators become more and more concentrated near the true value of the parameter being estimated

yup as clearly canadia states

But biasedness doesn’t determine consistency, an estimator can be unbiased and yet sill not consistent. In any case a sample can’t be biased; bias is a property of the estimator. Also consistency requires convergences in probability not convergence in distribution. Lastly it can’t " become consistent as n increases" since consistency is always referring to the value of the estimator at the prob limit when n goes to infinity, it is a property of the estimator (or series of estimators) at the limit. I could make my point more clearly: Increasing sample size increases the accuracy of the estimate for a consistent estimate (in some sense). What is increasing is accuracy not consistency.