Brian Galvin is the Director of Academic Programs at Veritas Prep, where he oversees all of the company's GMAT courses.
When you think about it, the authors of the GMAT are tasked with a pretty difficult initiative: using fairly common skills -- algebra, grammar, arithmetic, logic -- they need to write questions that will be difficult for large percentages of high-achieving examinees. Those taking the GMAT are already quite accomplished: college graduates, some already with graduate degrees, most with some quality post-college work experience, and all with a desire to pursue a higher level of education. Tricking this elite group of students is not easy!
The question writers do have a few built-in advantages that they'll employ to trap you, though, and one of them is the combination of a significant time limit for the exam and the tendency of multi-taskers to make time-saving assumptions to combat that pressure.
Consider the data sufficiency question:
How many integers x exist such that y < x < z?
1) z - y = 5
2) z + y = 7
First, it is important to know what the somewhat-convoluted question is asking; essentially, it wants to know how many values of x are between y and z (if y and z were 1 and 3, only 2 would be an integer between them, so the only possible value of integer x would be 2, and the answer to the question would be 1, as there is only one possible value).
Statement 1 provides a range for the difference between y and z; the two values are 5 numbers apart. Knowing this, you might plug in numbers to determine how many values are between them. If you were to use 6 and 1 (two numbers that are 5 apart), you'd find that there are 4 numbers between them: 2, 3, 4, and 5. Say you tried again with 100 and 95, there would still be 4 numbers (96, 97, 98, 99), and even using a negative number for one of the values (3 and -2, for which the difference is also 5), you'd find 4 values of x (-1, 0, 1, and 2). Based on this trial-and-error, you might be confident that there will always be 4 values of x, and you'd determine that statement 1, alone, is sufficient to answer the question.
This is a common reaction to this question -- but in your haste to select easy-to-calculate values of y and z, you may have forgotten that they do not need to be integers! Only x is specified in the question to be an integer, so you need to account for the fact that y and z could be nonintegers. If you do so, you could try 6.5 and 1.5, and you'd end up with 5 integers between them: 2, 3, 4, 5, and 6.
This assumption that a number must be an integer is common -- ask any child his favorite number, and he'll either respond with his favorite athlete's jersey number, or the day of his birthday, or some other common integer. No child will ever claim that his favorite number is pi, or -6! But ask that same child the rules of one of the classic childhood games -- Simon Says -- and he'll make sure that you understand that nothing is official unless Simon says it! Properties of numbers that we take for granted -- positive, integer -- are the GMAT version of Simon Says. You can't assume anything about a number on the GMAT unless you're explicitly told so.
To finish this question, statement 2 is not sufficient -- it doesn't even give a range for y and z. But taken together, the two statements allow us to solve for both y and z, giving us all the necessary information we would need (y is 6, z is 1, and therefore there are four possible values of x). C is the correct answer. More importantly, however, you should take note of the assumptions that you tend to make when working quickly -- the authors of the GMAT will hold those over you if you're not careful.
Veritas Prep probably has a GMAT prep class starting soon near you. Remember to use discount code GCLUB385 to take advantage of the 10% discount for all GMAT Club members!
