GMAT Tip of the Week: If At First You Don’t Succeed…

The GMAT is a fascinating exam for its ability to take fairly common concepts (algebra, arithmetic, logic) and turn them into devilishly-clever problems that stump high percentages of college-educated adults.  There are several familiar ways in which the GMAT does so:

– Forcing you to reverse-engineer a concept that you’ve always known from top-down

– Employing “complex” numbers or variables to disguise a problem that you’d ordinarily breeze through with smaller numbers

– Relying on your own mental inertia to distract you from the true matter at hand

– Creating problem setups that require your first 2-3 steps to feel “wrong”

This is by no means an exhaustive list, but it does show some of the common methods that the GMAT employs to keep you less-than-comfortable during the test. And, remember, it does all of this with a time limit and a long day’s worth of expended mental energy, compounding that difficulty.  Which is why it’s helpful to know the GMAT’s playbook going in to minimize stress and maximize efficiency.  So let’s talk about that last item and the GMAT’s tactics to force you to look failure in the eye right before you succeed.

Consider the problem:

If x, y, and z are all nonzero numbers and x = y + z, which of the following must be equal to 1?

(A) (y-z)/x
(B) (y-x)/z
(C) (z-x)/y
(D) (z-y)/x
(E) (x-z)/y

At first, this problem fits that “uses variables or hard numbers to make a common concept look hard” standard.  But you should soon note that some quick algebraic manipulation can set you on the course to make the given information look like an answer choice.  And the common thread with each answer choice is that each has a two-variable numerator and a one-variable denominator.  So your first inclination is almost always going to be to divide both sides by the single variable x:

x = y + z

1 = (y+z)/x

But this looks nothing like any of the answer choices.  You might even say that we’ve failed our mission – we changed the algebra in the way that we thought would answer the question and we may even be further from the answer now!  But look, now, at what’s missing: not only does each answer choice have a one-variable denominator, but they each have subtraction in the numerator.  So we need to rethink our approach to ensure that we have a subtraction-based equation before we divide one side by the other to reach 1.  So we can take the original:

x = y + z

and subtract y from both sides to get:

x – y = z

and then divide both sides by z to get:

(x-y)/z = 1

But again, we haven’t matched an answer choice.  Are we doing something wrong?  Why isn’t this working?

This is a classic GMAT device to try your patience.  If you know (as we do) that you’ve taken logical steps and it just hasn’t “clicked” yet, you’ll have the patience and confidence to give it one more round.  After all, we’ve tried 2 of 3 possible one-letter denominators.  We used x and z; the ever-crafty GMAT, of course, would pick y.  They know our predisposition for convenience (step one: just divide by the one-letter side that already exists) and for organization, this time in alphabetical order (ok, let’s then try x – y = z to keep the variables in order.  Knowing the GMAT’s style and knowing that we’re on the right track, we can remain calm and confident and make that one last attempt:

x = y + z

x – z  = y

(x-z)/y = 1 —> it’s answer choice E.

The GMAT is crafty — it knows how you think and knows that 2-3 steps of uncertainty or “failure” in a trial/error context is enough to unnerve or rattle a high percentage of test-takers. But the GMAT rewards you for confidence and patience.  So when manipulating algebra to try to make a more convenient statement, remember the old adage: if at first you don’t succeed, try, try again.  A 4-step process shouldn’t take anywhere near that average 2 minutes per question you want to spend on the quant section, but many examinees are content (or, rather panicked-enough) to quit when the 2nd or 3rd step doesn’t bear fruit.  Remember that about the GMAT — if you’re confident in your method, you’ll often need to carry that confidence through a few sticky-looking spots until the GMAT rewards you for perseverance.

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