I managed to see a word problem shown below:
" Mary obtained an average of 80 marks for 2 tests. What marks has she to get for an average of 80 marks for 3 tests?"
If a maths student understand the meaning of "average", she can do this without even working out the mathematical steps.
The first statement in the question stated that Mary scored on both tests an average of 80 marks. This implied that for one test, she obtained 80 marks. Same as for the second test.
For the next test (the third one), to get an average of again 80 marks, it meant that all the test she has to get 80 marks each. This is the power of "average". That is to say, all the test can be concluded as the same score.
The actual differences between the individual marks can be offset from each other to achieve a final "average" of same marks (here, 80 marks).
The maths problem is to test the understanding of the word "average" in maths, and its concept.
Thus, knowing concepts do help in solving maths questions.
It does not mean working out the mechanical computation steps to get answers.
With strong maths concept, anyone can solve simple problems without doing working.
But that is maths also (in the brain, the step-less way).
Interesting. Maths is so. Fear not.