Are HSK6 questions 51 through 60 (语病) so difficult that it's reasonable to just guess?
For native Chinese who read and write a lot, there are many obvious mistakes we can spot in one glance, but for learners, these questions are indeed extremely difficult.
Things that are easy to  spot:

保持年轻的 [之一秘诀] 是拥有健康的心态  --&gt; 保持年轻的 [秘诀之一] 是拥有健康的心态


&quot;XX 之一&quot; is a common structure for &quot;one of the XX &quot;

~

春天来了，到处是呈现出一片生机勃勃的景象。 --&gt; 春天来了，到处[是][呈现出]一片生机勃勃的景象。


是 is a verb, 呈现出 is also a verb. We only need one

The problem is not the difficulty. The problem is the long time it takes to go through the lengthy sentences.
Your teacher's suggestion was a practical one, for dealing with a time restrained test.
My suggestion is similar-- Answer the questions you know the answer first, leave the hard and long questions at the end.
Guess only at the last minute
Edit:
It took me 10 minutes to answer all ten questions. I guess non-native speakers would take three times as long. If a test has a time limit of two hours, and 200 questions, they would be spending  1/4 of their time to answer 1/20 of the questions.