To maximize your GMAT score, you need to be familiar with a few unconventional methods. Guessing and checking and following your intuition are methods that are neither as systematic nor as elegant as algebra, but they are your most valuable assets on the GMAT. During a timed test, doing algebra is often counter-productive because it is slow and error-prone. Instead, quick and decisive methods are your preferred, time-saving tactics.
This results from the structure of the GMAT itself. On the Quant, you’re only given two minutes per question, which elevates time management skills over math skills. This is precisely what the test-makers intended: as a business executive, the ability to recall math formulas is not as important as the ability to reason quickly. On the GMAT, then, half the battle is learning how to use valuable shortcuts effectively.
As an example, let’s take a look at the following data sufficiency problem:
Is b < ?
(1) b < a
(2) b = -2
A) Statement 1) alone is sufficient, but statement 2) alone is not sufficient
B) Statement 2) alone is sufficient, but statement 1) alone is not sufficient
C) BOTH statements 1) and 2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient)
D) EACH statement ALONE is sufficient
E) Statements 1) and 2) TOGETHER are NOT sufficient
To prove whether statement 1) or 2) is sufficient, you might be tempted to logically reason through each statement. You could set up inequalities, perhaps perform some substitution or logical reasoning, and then manipulate the inequalities to fit your proof. Such an approach, however, would likely exceed five minutes, and might possibly be riddled with careless errors. For these reasons, you should ignore traditional methodology and instead use some unconventional methods. First up, let’s follow our intuition.
Just by looking at statement 1) alone, we can probably suspect that it provides insufficient data. We’re told that b < a, but that seems to tell us very little about whether b < . After all, we don’t know whether the variable “a” is positive or negative, and the exponent in can change “a” from a negative number to a positive number. We can’t prove this suspicion for certain, since it was merely an educated guess, but we now have a starting point. If statement 1) alone is insufficient, we can prove this without doing any algebra simply by demonstrating a contradiction.
Demonstrating a contradiction is a powerful technique for data sufficiency questions on the Quant. For a statement to provide sufficient data for a Yes/No-type DS question, it must guarantee that the answer to the question stem is either always “Yes” or always “No”. In this problem, statement 1) would provide sufficient data if we could prove that b < is always true, or always false. If we can find even one single set of contradictory examples, so that the answer is at times “Yes” but at times “No”, we have proven that the statement is insufficient. Demonstrating a contradiction obviates the need for algebra altogether — all we need is a single set of examples that fit the statement, yet give contradictory answers to the question stem.
We’ll use the technique of plugging-in to find two contradictory examples. For the first example, let’s choose a few small prime numbers, such as a = 3 and b = 2. If we plug these numbers in, we see that b < a, so these numbers satisfy statement 1). Now, let’s answer the question stem: is b < ? We see that 2 is indeed less than = 9, so the answer is “Yes”.
We now need to find a single example of a contradictory “No” answer to the question stem. To do so, let’s switch the type of numbers used for the plug-in. We used positive, prime integers at first, but there are no restrictions which state that the numbers must be positive values — or even integers. We should therefore consider using fractions or negative numbers.
Let’s try one set of fractional plug-ins: b= and a=. We see that it satisfies statement 1), but because is not smaller than , we have a “No” answer to the question stem. With two answers that lead to contradictory results (sometimes “yes”, other times “No”), we have insufficient data. We can eliminate choices A/D, all without touching even the slightest bit of algebra.
In general, if your hunch suggests that you have insufficient data, avoid algebra. Prove you have insufficiency by demonstrating a contradiction by plugging-in a few numbers. Only use algebra if you suspect you have sufficient data.
For the following questions, I’d like you to try to solve the problem by avoiding algebra whenever possible. Instead, try to demonstrate a contradiction to prove that you have insufficient data:
Is || > ||?
(1) x > y
(2) x > 0