GMAT Data Sufficiency: Three Patterns with Test Day Shortcuts
June 8, 2011
By Guest Author Eli Meyer
Kaplan recommends that students begin to solve GMAT Data Sufficiency problems at the question stem. The stem often provides vital information, and without understanding the question itself, it’s impossible to accurately evaluate the statements. However, sometimes question stems can be complex and impenetrable, especially if you’re behind schedule and the clock is ticking. In those cases, the statements can help you make an educated guess about possible answers. There are three patterns of Data Sufficiency statements that can narrow down the information, each of which involves overlapping information between statements, or between a statement and what you already know from the stem or common sense. Recognizing these patterns can be a useful time saver on test day.
Pattern I: Identical statements
1) 2x + 3y = 6
2) 6y = 12 – 4x
The GMAT will never literally repeat a statement, but it might give two statements that provide identical information. For example, “50% chance of heads” and “50% chance of tails” are, on a fair coin, exactly equivalent mathematically. Or, as above, if you add 4x to both sides of statement 2:
6y + 4x = 12
and you then divide both sides by two:
3y + 2x = 6
you will find that the two statements provide the same information.
When the statements are identical, it’s impossible for one statement to be sufficient without the other also being sufficient; similarly, combining them can’t ever help because we are just taking the same info twice! Regardless of the question stem, the answer must be (D) or (E) in this specific scenario.
Pattern II: One statement implies the other
1) x is positive
2) x is prime
Sometimes, one statement provides enough information by itself to make the other redundant. For example, in the case above, prime numbers are (by definition) positive. Normally, Kaplan recommends that students evaluate the statements one at a time, but in this case one statement includes all the information of the other statement. Other examples: “1) x > 4” implies that “2) x > 2”, and “1) y is even” must be true whenever “2) y / 2 is even” is true. When we recognize this pattern, we can eliminate two answer choices. In our first example, if knowing x is positive is enough to answer the question, then knowing x is prime tells us x is positive and so is also sufficient. 1) can never be the only sufficient statement, and (A) can never be the answer, regardless of the question stem. On the other hand, if knowing x is prime is insufficient, then telling as that x is also positive adds literally no information. Statements 1) and 2) combined are exactly equivalent to statement 2) alone. If 2) alone is insufficient, we will not get any additional help from statement 1), so the answer can never be (C) in this scenario.
Pattern III. One statement you already know
1) If Suzie drove 5 miles per hour faster, she would have arrived 1 hour sooner.
2) If Suzie had driven twice as fast, she would have arrived in half the time.
Sometimes a statement will tell you something you already know. This might be because it overlaps with information from the question stem. Other times, as above, the statement is just telling you a mathematical tautology. If we convert statement 2 into algebra, Distance = (2* Rate)* (Time/2). We are multiplying and dividing by 2, so we can cancel the 2′s to give us D = R * T. This is the rate formula which we already know. Whenever you double the speed you halve the time, regardless of the original distant, speed, or rate!
Statement 2) in this case is worthless. We can rule out any answer choice that involves statement 2) being sufficient, or even contributing to sufficiency. In the above example, either 1) is sufficient or it isn’t; our only answer choices are (A) and (E).