Is it possible that Pearson's Chi - squared test and likelihood ratio test (-2logΛ) for goodness of fit to give different results for the same data? i.e one test to show that the data are consistent and the other test to show that the data are not consistent with a given model?

I had been doing my calculations for an exercise and the two tests give different results, although we have learned that -2logΛ is an approximation to Pearson's Chi - squared test.

An answer to my question would be very helpful