Whenever you’re picking numbers on a Data Sufficiency problem, you have to keep one image in your mind: Snoop Dogg at a limbo contest. How will that help you master Data Sufficiency? How can the Doggfather help you beat the Testmaker? Well think about the two questions that Snoop would be asking himself constantly at such a contest:
1) How high can I get? (Snoop’s general state of mind)
2) How low can I go? (Because you know Snoop’s in it to win it)
And that mindset is absolutely crucial in a Data Sufficiency number-picking situation. On these problems, the GMAT Testmaker knows your tendencies well: you’re predisposed to picking numbers that are easy to work with. Consider an example like:
If x is a positive integer less than 30, what is the value of x?
(1) When x is divided by 3 the remainder is 2.
(2) When x is divided by 5 the remainder is 2
On this problem, most can quite quickly eliminate statement 1, as x could be 5, 8, 11, 14, 17, 20, 23, 26, or 29. Typically your quick-thinking methodology will have you look at 3, then add the remainder of 2 (producing 5), then start looking at other multiples of 3 and doing the same (6 + 2 gives you 8, 9 + 2 gives you 11, and so on).
And similarly you can apply that logic to statement 2 and eliminate that pretty quickly. The obvious first candidate is 7 (add the remainder of 2 to 5), and then you should see the pattern: 7, 12, 17, 22, and 27 are your options.
So when you look at these quick lists and see that the only place they overlap is 17 (17/5 is 3 remainder 2 and 17/3 is 5 remainder 2), you might opt for C.
But where does Snoop Dogg’s Limbo Contest come in? Look at the range they gave you: a POSITIVE INTEGER (so anything > 0) LESS THAN 30 (so anything <30). So when you combine those, your range is 0 < x < 30. Then ask yourself:
*How high can you get? Well, on either list you’ve gotten as close to 30 as possible. The next possible number on the first list (5, 8, 11, 14, 17, 20, 23, 26, 29…) is 32, but they tell you that x is less than 30 so you can’t get that high. And the next possible number on the second list (7, 12, 17, 22, 27…) is also 32, but again you’re not allowed to get that high. So you’ve definitely answered that question well.
*How low can you go? On this one, you haven’t yet exhausted the lower limit. Look at the patterns on those lists – on the first one, all numbers are 3 apart but you started at 5. If you move down 3, you get to 2 (2, 5, 8…). And 2/3 is 0 remainder 2, so 2 is a legitimate number on that list, a positive integer that leaves a remainder of 2 when divided by 3. And on the second list, you started at 7 and kept adding 5s. Move 5 spots to the left and you’re again at 2, which does leave a remainder of 2 when divided by 5. So upon closer examination, this problem has two solutions: 2 and 17.
The GMAT does a masterful job of setting ranges that test-takers don’t exhaust, and that’s where the Snoop Limbo mentality comes into play. If you’re always asking yourself “how high can I get and how low can I go?” you’ll force yourself to consider all available options. So for example, if the test were to tell you that:
x^2 < 25 –> This doesn’t just mean that x is less than 5 (how high can you get) it also means that x is greater than -5 (how low can you go)
x is a positive three-digit integer –> make sure you try 100 (how low can you go) and 999 (how high can you get)
x > 0 –> You might want to start with 1, but make sure you consider fractions like 1/2 and 1/8, too (how low can you go? all the way to 0.00000….0001), and try a number in the thousands or millions too (how high can you get?) since most people will just test easy-reference numbers like 1, 2, 5, and 10. A massive number might react differently.
In triangle ABC, angle ABC measures greater than 90 degrees –> remember that “how high can you get” is capped by the fact that the three angles have to add to 180, but this obtuse angle can get up even above 179 (how high can you get?)
x is a nonnegative integer –> the smallest integer that’s not negative is 0, not 1! How low can you go? You’d better check 0.
3 < x < 5 –> it doesn’t have to be 4, as x could be 3.0000000001 or 4.99999999
So keep Snoop’s Limbo Contest in mind when you pick numbers on Data Sufficiency problems. Don’t just pick the easiest numbers to plug in or the first few numbers that come to mind. The GMAT often plays to the edge cases, so always ask yourself how high you can get and how low you can go.
(and for our readers who prefer East Coast rap to West Coast rap, feel free to substitute this with the “Biggie (how big a number can you use) Smalls (how small a number can you use)” method and you can end up with a notoriously big score).
By Brian Galvin