“Officer, I didn’t know I couldn’t do that,” Dave Chappelle’s friend, Chip, told a police officer after being pulled over for any number of reckless driving infractions. In Chappelle’s famous stand-up comedy routine, he mocks the audacity of his (privileged) friend for even thinking of saying that to a police officer. But that’s the exact type of audacity that gets rewarded on Data Sufficiency problems, and a powerful lesson for those who, like Dave in the story, seem more resigned to their plight of being rejected at the mercy of the GMAT yet again.
How does Chip’s mentality help you on the GMAT? Consider this Data Sufficiency fragment:
Is the product of integers j, k, m, and n equal to 1?
(1) (jk)/mn = 1
The approach that most students take here involves plugging in numbers for j, k, m, and n and seeing what answer they get. Knowing that jk = mn (by manipulating the algebra in statement 1) they may pick combinations:
1 * 8 = 2 * 4, in which case the product is 64 and the answer is no
2 * 5 = 1 * 10, in which case the product is 100 and the answer is no
And so some will, after picking a series of arbitrary number choices, claim that the answer must be no. But in doing so, they’re leaving out the possibilities:
1 * 1 = 1 * 1, in which case the product jkmn = 1*1*1*1 = 1, so the answer is yes
-1 * 1 = -1 * 1, in which case the product is also 1, and the answer is yes
And here’s where Chip Logic comes into play: in any given classroom, when the two latter sets of numbers are demonstrated, at least a few students will say “How are we allowed to use the same number twice? No one told us we could do that?”. And the best response to that is Chip’s very own: “I didn’t know I COULDN’T do that.” Since the problem didn’t restrict the use of the same number twice (to do so they might say “unique integers j, k, m, and n”), it’s on you to consider all possible combinations, including “they all equal 1.” Data Sufficiency tends to reward those who consider the edge cases: the highest or lowest possible number allowed, or fractions/decimals, or negative numbers, or zero. If you’re going to pick numbers on Data Sufficiency questions, you have to think like Chip: if you weren’t explicitly told that you couldn’t, you have to assume that you can.
So on Data Sufficiency problems, when you pick numbers, do so with a sense of entitlement and audacity. Number-picking is no place for the timid – your job is to “break” the obvious answer by finding allowable combinations that give you a different answer; in doing so, you can prove a statement to be insufficient. So as you chip away at your goal of a 700+ score, summon your inner Chip. When it comes to picking numbers, “I didn’t know I couldn’t do that” is the mentality you need to know you can use.
By Brian Galvin