Solution requires more details
Fragment of a discussion from Science talk:Math Exam Resources/Courses/MATH221/December 2008/Question 03 (a)
You are absolutely right, on hindsight it's not a clean/clear argument at all (I was a little too eager in avoiding calculations!), and certainly the most straightforward solution is the one above. In view of this, I am in agreement and will remove and replace with the latter as you suggest.