the nona wrote:When is it favourable to use backsolving ? when is it favourable to use estimation ? and when is it favourable to plug numbers ? apart from the problems with variables in answer choices of course .

Thanks in advance

It is difficult to categorize GMAT problems on the basis of solution approaches. Most of the problems can be solved by more than one approaches. Ultimately it depends upon your experience and your judgement on the test day.

Still I'll try to give a general idea.
And I'll update this post with more examples and more points if I can think of.

Back Solving or Plugging Options:
This is mostly applicable for PS problems which asks for the value of a certain quantity such that you can form an algebraic equation for it. For example, the following problems can be solved by back solving or plugging the options,
https://www.beatthegmat.com/official-que ... tml#630390
https://www.beatthegmat.com/what-is-valu ... 94144.html
https://www.beatthegmat.com/managers-t210717.html

Often back solving becomes easier (and sometimes feasible) if we setup a simplified algebraic equation. For example,
https://www.beatthegmat.com/og-137-t222499.html#629178

But some problems (e.g. probability or combinatorics problems) cannot be solved by back solving. Example of such problems,
https://www.beatthegmat.com/probability- ... tml#616173
https://www.beatthegmat.com/interesting- ... tml#616160

Another example I can think of...

If y = 4x³ + 11x² + 5x - 2, what is the value of x for which y becomes zero?

The above problem can be easily solved by plugging the provided options as the value of x and checking whether y = 0 or not. But if the problem is modified as follows,

If y = 4x³ + 3x² - 6x + 5, what is the sum of the values of x for which y becomes zero?

Now, we cannot solve this problem by plugging the options.

Estimation:
This is mostly applicable for problems where the options are not close numbers or the problem asks for an approximate answer or the problem involves heavy calculation. For example, the following problems can be (and sometimes, should be) solved by approximation,
https://www.beatthegmat.com/suggest-some ... tml#620216
https://www.beatthegmat.com/how-to-solve ... tml#630050
https://www.beatthegmat.com/manhattan-gm ... 99803.html

Tip : For problems with heavy calculation, always try to approximate by rounding up or down the numbers. And for fractions, if round up the numerator then round down the denominator and vice versa.


Plugging Numbers:
This is mostly applicable for problems where everything is in reference with some unknown, i.e. there are no definite quantities. For example, word problems involving percentage and fractions or problems where everything is in terms of variables. For example,
https://www.beatthegmat.com/gmat-prep-qu ... tml#630398
https://www.beatthegmat.com/how-much-was ... tml#622545

Tip #1: For problems involving percentage, plug in 100 (or multiples of 100) for the total quantity.
Tip #2: For problems involving fractions, plug in the LCM of the denominators of all the fractions for the total quantity.
Tip #3: For problems involving variables, plug in some simple values (like 0/1/2 etc) for the variables and cross check the options by evaluating for the same values. Also, remember to check all the options as it is possible that for the particular number you have plugged, more than one option may work.
For example,
https://www.beatthegmat.com/133-qant-gui ... tml#630717
https://www.beatthegmat.com/grade-of-mil ... tml#633610


Apart from these, another technique is:
Eliminating the Wrong Options: For some problems, if you look carefully you can discard all the wrong options by some logic like divisibility or units digit. For example,
https://www.beatthegmat.com/a-group-of-n ... tml#611732
https://www.beatthegmat.com/manhattan-ca ... tml#449510
https://www.beatthegmat.com/the-measures ... tml#627814

Hope that helps.