IanStewart wrote:
beyondgmatscore wrote:
The plugging-in works only because the options are of a certain nature. What if all the options satisfied the condition involving being multiples, then we would end up doing the plugging in first and then come back to solve the algebraic equation. Just because plugging in works sometime doesn't mean it is always the optimal and fastest way. If the algebraic method just involves solving a simple quadratic equation, then it is GUARANTEED to give an answer in under one minute, whereas plugging-in may take less than that or greater than that depending on the kind of options that are there. So, as a rule, if I can quickly get the answer following a general algebraic principle, I would always prefer that over plugging in the numbers.
If you look at this question:
difficult-ps-problem-help-100767.htmlwhich is in essentially the same format as the one in the original post above, the algebra is considerably more time consuming than using the answer choices and divisibility properties. Using divisibility (we want to get an integer when we divide 90 by the right answer, and by the right answer plus 0.5) you can get the answer within a few seconds.
I've mentioned quite a few times that I think the usefulness of backsolving is vastly overstated in many prep books. For most GMAT questions, you end up solving the same problem several times, rather than once, when you backsolve, so it's typically a very inefficient approach. However, for questions in the very specific format of the one in this post, I find backsolving to be much faster than any direct algebraic approach, provided you use number theory to zero in on the correct answer. In most questions of this type, only one answer is even plausible when you apply divisibility principles, so you can often pick the right answer without doing any calculation. The algebra is never quite that fast.
Ian - I think both of us are saying the same thing - Having backsolving as your primary technique would lead to more situations where we would end up solving the problem multiple times. I am all for being smart in reducing the steps in algebra, but a little hesitant on relying on backsolving as a primary method. for.e.g. in the above problem that you linked to, if my answer choices were such that 2.5 was at the end and if 4.5 was listed as one of the choices (which also gives integer when 90 is divided by it and 4.5+0.5 = 5.0 also yields an integer) then we would need to resort to algebra anyway AFTER spending considerable time in plugging in - and we have no way of knowing before we start plugging in that divisibility condition would be met by just one of the choices.
As per algebra there, we quickly get the equation as v^2-9 = 1080 or (v+3)*(v-3) = 36*30 and hence v = 33. Personally, I find this more intuitive and predictable way of solving it then to try and check various choices.
But then again, one should stick to what works best for them - its just that I prefer a more predictable method than the one where examiner has the ability to fox me by giving options that rule out back solving or plugging in and discover the same after spending time trying to back solve.