2 min question again :)

VP_RedSoxFan wrote:My only caution about backsolving is when we start with assumptions like, since the patio is square, the answer must likely be a perfect square. In this problem, x can be solved for as x=3 so it works out, but a different solution of x could have actually precluded it from being a square. Then we would have spent a minute or 2 testing 3 answers that couldn't be correct, finish without a conclusive answer and then retest assuming we'd made an error somewhere in those 3 even though our error could have been in assuming it was a square in the first place.

I also am leery of backsolving as a main strategy because it lends itself to a lot of computation, and, thus, careless errors.

Learning to move through the algebra on a problem like this (the hardest part is factoring 4x^2+5x-66=0 into (4x+22)(x-3)=0) is a worthwhile endeavor--one that pays off on test day for this and other problems like it. I'd guess that without a strong command of algebra and problem solving skills like the ones tested on this problem, you have a much lower ceiling for a overall score.

Just my humble opinion....

I agree with Ryan here- actually, I will be much less diplomatic about this strategy. Backsolving is normally a huge waste of time on the GMAT- you often end up solving the same problem two or three times, when algebra would get you to the solution the first time. If you can do the algebra, you'll do much better on the test. Backsolving only lends itself to word or algebra problems with numerical answers, and you won't see many of those past the 550 level; it's a low-level technique, and should only be viewed as a fallback strategy. If you're stuck, definitely use it, but it should not be the first thing a well-prepared GMAT taker should think to do. If you're aiming for a 700, these kinds of 'tricks' won't get you there; you need to know some math.

The problem in the OP does not look like a real GMAT problem (the algebraic result is too complicated to solve quickly)- it reads like a test prep company problem. Test prep company questions are often not a good guide to what you'll see on the real GMAT test- companies manufacture problems to illustrate the efficacy of their strategies. Look at the OG or the GMATPrep software, and judge for yourself how useful backsolving is- there are close to no problems, at least past the easy stage, from official materials that are best solved by backsolving (excluding problems which explicitly force you to backsolve, like 'which of the following is largest?').

Stuart Kovinsky wrote:I'm going to vehemently disagree.

That doesn't surprise me!

Stuart Kovinsky wrote: Backsolving is a fantastic strategy. I'm great at math, yet there are still many questions that I find it quicker to backsolve. The answers are incredibly powerful tools on a multiple choice test and anyone who ignores them wilL NOT hit his or her highest potential score.

The answers are often very valuable- we agree there- but that's not, in most cases, because they enable backsolving. There are many other ways to use answer choices to your advantage on the GMAT, which I may go into in another post.

Is backsolving a 'fantastic strategy'? I said in my last post that it is not normally a good strategy to use at the higher levels of the test. Take a sample of difficult GMAT questions- I just looked at questions 200 through 249 in the Problem Solving section of the orange Official Guide. Of these 50 questions:

• 14 questions could, in theory, be solved by backsolving;
• the only question where backsolving seems a good approach is number 200, and even there, the algebra is simple: the time required is equal either way. There are three that some might find debatable:
• Someone stuck on question 223 might backsolve, but this is such a common question type that a well-prepared test-taker should have a much quicker strategy here (subtract the speeds);
• Question 228 can be backsolved, but the answer choices are the only plausible answers, so seeing them is not very helpful;
• Question 232 can be backsolved, but the algebra is very fast;
• On questions 205, 210, 211, 213, 220, 222, 235, 237, 238, and 240, if you choose to backsolve, you are spending more time than you should. In these questions, if you backsolve, then for each answer choice you need to test you are doing the same steps (in reverse) as you would do if you solved the question algebraically. The algebra gives you the answer on the first try, while by backsolving you may need to do the same question several times over. Worse still, on some questions this can lead to very time-consuming calculations (213, 238, among others).

In brief: if this sample is representative, someone doing well on the GMAT may have the option to backsolve on about a quarter of Problem Solving questions-- six or seven questions on a complete test (of course, you can't backsolve a Data Sufficiency question). However, it's only a time-neutral strategy on 2% (well, if I'm charitable, 4% or 6%) of Problem Solving questions. That's between 0.5 and 1.5 questions on a given GMAT. It is almost never time-efficient.

This is why I said, in my previous post, that backsolving is a low-level strategy; it can be used to answer questions, but it is rarely the best approach, at least if you're aiming for an elite GMAT score. There's no harm in learning how to do it- there's really nothing to learn. And backsolving is a good fallback if you can't do a question directly- much better to backsolve than to guess randomly, of course. But if you can do a question directly, it is almost always best to do so on difficult GMAT questions.

More importantly, however- going by the Official Guide, roughly three quarters of hard GMAT problems are entirely immune to backsolving. For these, you need to have some conceptual understanding of mathematics, need to be able to handle abstraction, and need to be able to set up equations. To do well on these questions, you need to learn math- 'tricks' won't help.