chrtpmdr wrote:
How to you avoid taking too long on factoring the quadratic equation?
I somehow always slightly get stressed when I don't have a first sight quadratic equation and I tend to overcomplicate, even though this one was quite solvable.
Hello chrtpmdr,
In my opinion, you should
never try to SOLVE an equation, whatever type it may be, on a GMAT Quant question.
In questions on equations, very often we solve to find the unknown/s. As such,
the answer options given with the question will also represent the value of the unknowns we are trying to obtain. Therefore, solving a linear equation/quadratic in the step-by-step approach, by factorizing/taking things common/solving them as simultaneous equations smacks of a very ‘text-book’ kind of approach.
That’s not what GMAT is testing you on. Sure, GMAT expects you to be able to develop variables, construct equations and solve them. But it does not expect you to solve them in a certain set way. In fact, it probably wants you to try out innovative approaches by plugging in values – based on your judgement or from the options.
If you look at Cubic equations, there’s absolutely no way of knowing the first root until you plug in values like 0, 1 and -1. So,
you need to understand that Math alone will not help you ace topics in GMAT Quant. You need to put on your logical reasoning hat as well.
But, unfortunately, that’s the bane of many test takers. They end up depending too much on Math to bail them out. They end up assuming that, solving an equation a particular way it was taught in school, is the best way of solving it. Really, there is no pride in solving equations the conventional way IMHO. I’d rather leverage the answer options and logic to figure out which options may fit in. I’d rather use the time to do this than breaking my head about the factors.
To answer your question about how to quickly factorise, you need to observe the constant and think of all the ways in which you can break it down into a product of 2 of its own factors.
For example, 120 = 20*6 / 30*4/12*10/15*8/24*5/60*2/120*1/40*3.
When you do this, it will become easy for you to pick the pair that will give you the middle term when added. I’m not saying that you will have to write out all the pairs all the time. If you inculcate this habit when you are starting off with your prep on Quadratics, by the time you factorise 10 to 15 quadratics, this would probably have become muscle memory for you. And that’s
the idea of prepping for GMAT, building good muscle memory. If you did not want to deal with this quadratic, you could have dealt with the more preliminary equation which has been equated to 420. Observe that, out of the options,
only 28 and 30 are factors of 420. Remember that we are trying to find the number of calculators (which cannot be a fraction), so
I’d naturally chose 30 since (30-2) should also be a factor of 420. Note that this happened more sub-consciously with me because of my muscle memory.
So, it’s really not about being strong with Math alone. If you think of it that way, I’d not be surprised if you are stressed in such situations. From now on, try to incorporate a few of these things in your Quant prep and you will see yourself saving on time on effort.
Hope that helps!
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