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One of the most widespread mistakes I see students make on Data Sufficiency concerns the information they consider when evaluating a statement. To properly determine whether a statement is sufficient, you must be focused on using only the information given. If, for example, a statement only tells you that -10 < x < 10, but says nothing else, then you can’t assume that x is an integer, and you can’t assume that x is positive. Recognizing that students who rush through the questions will often fill in the gaps with their own assumptions, the test-makers create questions specifically designed to mislead those who fail to consider all the possibilities that can be gleaned from a statement. Let’s look at a sample question to see how this mistake might manifest itself.
If x, y, and z are three positive integers, are they consecutive integers?
1) z – x = 2
2) x < y < z
As with any Data Sufficiency question, our first step should be to identify what information the prompt provides us. In this case, we know that x, y, and z are all positive and all whole numbers. Our next step, like always, is to attempt to simplify the question in the prompt. In this case, nothing stands out that can be simplified, so let’s jump into the statements.
Statement 1 tells us that z – x = 2.
What can we deduce from this? We know that z is 2 units ahead of x on the number line and that both variables represent integers. But what about y? The prompt presents the integers in the order of x, y, and z, so it would appear safe to assume that y falls in the middle of the sequence and would thus be one integer away from each of the numbers. So, according to this logic, if x = 2 and z = 4, then y must equal 3, and the three integers are consecutive. But this is where your assumption will lead you astray! Though the prompt presents the variables in the order of x, y, and z, it gives no indication that these numbers are necessarily in that order. If they are not in that order, then y could very well be 1,000,000 while x = 2 and z = 4. In this case, the three integers would not be consecutive, contrary to what we had assumed upon first reading the statement and looking back at the prompt. So, though, upon a superficial glance, it would appear that the statement is sufficient, a more thorough inspection reveals that it gives more than one answer to the prompt. Thus, it is insufficient. The answer is B, C, or E.
Statement 2 tells us that: x < y < z
This statement provides us with the information we were missing in Statement 1, namely that x, y, and z go in order from least to greatest. However, the statement does not tell us whether these numbers are spaced by 1. They might go up in the order of 1,2, 3, in which case they would be consecutive integers. But it might turn out that x = 1, y = 2, and z = 1,000,000, in which case they would not be consecutive. Since the statement gives contradictory answers to the prompt, it is not sufficient. The answer is C or E.
Now, let’s combine the statements. Recall that Statement 1 was insufficient because we couldn’t assume that y is between x and z. How does Statement 2 help? It provides us with that exact information! Now that Statement 2 provides the very information that we had assumed in Statement 1, we can be sure that both statements combined will be sufficient. Thus, the answer is C.
What’s particularly interesting about this question is the insight it provides into the minds of the test-makers. Data Sufficiency questions are primarily concerned with your ability to assimilate new information and understand its implications. When doing so, one of the common pitfalls people experience (both in everyday life and on the GMAT) is filling in the gaps with information that does not exist. Though it’s tempting to let your mind relax and make what appear to be logical assumptions, success on the tougher GMAT questions will stem largely from your ability to work only with the information presented to you.