GMAT Tip of the Week: The Heart of Data Sufficiency

GMAT Tip of the WeekData Sufficiency is a game as much as it’s a “problem.” Look at the statistics in the Veritas Prep Question Bank and you’ll see that most Data Sufficiency questions are created with a particular trap answer in mind and that at least 1-2 answer choices are rarely-if-ever chosen.

For example, look at these graphs:



In the first graph, the answer is E but the author desperately wants you to pick C. In the second, the answer is B but the author is baiting you hard into picking C. And in the third, the answer is C but the author is tempting you with E. In any of these cases, the strategy behind the question is as important – if not more important – than the math itself. Because it’s usually fairly easy for an average (or below) student to eliminate 1-2 answer choices on Data Sufficiency questions, the authors have to “get their odds back” through gamesmanship, by showing you a statement (or two) that look one way (sufficient or not) but that act counterintuitively. And to understand how to play this game well, it may be helpful to see Data Sufficiency through the lens of another popular game, the card game Hearts.

In Hearts, the goal of the game is to avoid getting “points”, and you get points when you end up with any hearts (one point each) or the Queen of Spades (13 points) after having taken a trick. And like with Data Sufficiency, there are really two ways to play: the way you’d play with a middle-schooler who’s learning the game, and the way you’d play with a group of adults who are each trying to win.

Playing Hearts with kids is like doing Data Sufficiency questions below the 550 level – you pretty much just play it straight. In Hearts, that means that when you don’t have any cards of the suit that was led, you try to get rid of your highest point-value cards immediately. If clubs are led and you don’t have clubs, you either get rid of the Queen of Spades if you have it, or you pick your highest heart and unload that. Your goal is to get rid of high cards and point cards quickly so that you end up with as few points as possible.

But if you’re playing with adults, you have to consider the possibility that someone may be trying to “Shoot the Moon” – getting *all* of the points cards in which case they get 0 points and every other player gets 26. What might seem like a counter-intuitive strategy to a 12-year old is often quite necessary when you suspect an opponent may be trying to shoot the moon: even though you may have a chance to get rid of your king-of-hearts, you might hold on to it because you want a high heart in case you need to “win” one of the last tricks to stop the opponent from getting all of the hearts. When you’re playing with adults (or attempting Data Sufficiency questions in the high 600s and into the 700s), you need to see the game with more nuance and develop an instinct for when to avoid the “obvious” play to save yourself from a more-catastrophic outcome.

This is especially true when you notice something suspicious from your opponent; if in one of the first few hands an opponent leads with, say, the jack of hearts, that’s a suspicious play. Why would she fairly-willingly open herself up to taking four points? Or if the first time a heart is played, an opponent swoops in with a high card of the suit that was led, but you know they probably have a lower card that would have let them avoid taking the heart, you again should be suspicious. In either of these cases, an astute player will make a mental note to hold back a high card or two just in case shooting-the-moon is in play. Playing hearts as an adult, you’re often playing the opponent as much as you’re playing the cards.

How does this apply to Data Sufficiency?

Consider this question:

Is a > bc?

(1) a/c > b

(2) c > 3

Playing “middle school hearts”, many test-takers will run through this progression:

Step one: If you multiply both sides by c, you get a > bc so this looks sufficient*. The answer, then, would be A or D.

Step two: Forget everything you learned about statement 1 since you’ve already made your decision about it. Statement 2 is clearly insufficient on its own, so the answer must be A*.

(*we know the math here is slightly flawed; demonstration purposes only!)

But here’s how you’d play the game as an adult, or as a 700-level test-taker:

Step one: Same thing – if you multiply both sides by c you’ll get a > bc, so this one looks sufficient.

Step two: Wait a second – statement 2 is absolutely worthless. And statement one wasn’t *that* hard or interesting. Maybe the author of this question is “shooting the moon”…

Step three: Look at both statements together, reconsidering statement 1 by asking myself if statement 2 matters. If statement 2 is true and c is, say, 10, then a/10 > b would mean that a > 10b, so this still holds. But what if c is -10, and statement 2 is not true. a/(-10) > b would mean that when I multiply both sides by -10 I have to flip the sign, leaving a < -10b. This time it’s not true. Statement 2 *seems* worthless but in actuality it’s essential. Statement 1 is not sufficient alone; as it turns out I need statement 2.

What’s the difference between the two methodologies?

The 500-level, “middle school hearts” approach – NEVER consider the statements together unless they’re each insufficient alone – leaves you vulnerable to the author’s bait. On hard questions, authors love to shoot the moon…that’s their best chance of tricking savvy test-takers.

The 700-level, “playing hearts with grownups” approach seems counterintuitive, much like saving your king of hearts and knowingly accepting points in a hearts game would seem strange to a seventh-grader. But it’s important because it saves you from that bait. On a question like this, it’s easy to think that statement 1 is sufficient; abstract algebra is great at getting your mind away from numbers like negatives, zero, fractions… But statement 2’s worthlessness (ALONE) functions two ways: it’s a trap for the unsuspecting 500-level types, and it’s a reward for those who know how to play the game. That worthless statement 2 is akin to the author leading a high heart early in the game – the novice player sees it as a freebie; the expert considers “why did she do that?” and re-examines statement 1 by asking specifically “what if statement 2 weren’t true; would that change anything?”.

Remember, when you’re taking the GMAT you’re playing against other very-intelligent adults, and so the authors of these questions have a responsibility to “shoot the moon”. While the rules of the game dictate that you don’t want to consider the statements together until you’ve eliminated A, B, and D, there’s a caveat – if you have reason to believe that the author of the question is trying to trick you (which is very frequently the case on 600+ level questions), you have to consider what one statement might tell you about the other; you have to play the game.

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By Brian Galvin