Math on the GMAT can be hard enough when it is presented without trickery. However, the test-maker knows that even simple math can be made challenging by including complex verbal descriptions or by disguising one mathematical concept as another. Kaplan considers paraphrasing one of the core competencies necessary to crack the GMAT, and this is never more true then when you are approaching complex Data Sufficiency question stems.
At the most basic level, you should ‘paraphrase’ any algebraic word problems in DS question stems as mathematical equations. Consider the following DS stem:
Prior to a reorganization, every manager in a company supervised 17 workers. Under the new company structure, several new managers were hired, and each manager now supervises 14 workers. If the number of workers did not change, how many managers were there after the reorganization?
Inexperienced and overeager test-takers may jump straight to the statements from here, but it’s worth the time to analyze this. We have three variables—the number of managers Before the reorganization (we’ll call this B) and the number of managers After (A), and the unchanging number of Workers (W). We also have to ratios, which we can write out as follows:
17A = W
14B = W
And our question:
A = ?
Well, wait a second. We know this rule—three variables, two equations. The n-variables n-equations rule tells us that all we need is one more equation, any equation, for sufficiency! So, while other test-takers may be struggling to plug in actual values or to get a number solution, we’ll be able to tell at a glance that
1) There are 714 workers at the company
2) 9 new managers were hired by the company
are both sufficient! They both give us a third equation to complete our system of three variables, and so the answer must be (D)
Paraphrasing can be more than just simplifying, however. Number properties questions, in particular, give skilled test-takers a chance to recognize a mathematical concept that’s hidden from plain view. Consider this problem:
Is 6 + n/8 an integer?
Looks like a fraction problem, right? That’s what the test-makers want you to think! But this first impression doesn’t withstand scrutiny. The key deduction is that an integer plus an integer will always be an integer, and an integer plus a non-integer will always be a non-integer. Or, to put it another way, that 6 is irrelevant! We get the same answer with 100 + n/8 or, more usefully, 0 + n/8. So really, all we care about is this:
Is n/8 an integer?
But wait. This isn’t a fraction problem at all. In fact, when asking if a variable divided by a number is an integer, we’re really dealing with divisibility rules. So, we can paraphrase the question as follows:
Is n divisible by 8?
Rephrasing the question makes the statements much easier to analyze. If our statements look like this:
1) n is even
2) n divided by 8 has a remainder of 2
Then we can see right away how the paraphrasing helps us! These rules have nothing to do with the fraction problem that this question was disguised as, and everything to do with divisibility. We can evaluate them much more effectively having paraphrased the stem. Statement 1) doesn’t help, since n could be 2 or 8, “No” or “Yes.” (Remember, on a Yes/No question, whenever the answer is “Maybe” the statement is insufficient!) However, statement 2) will never be divisible by 8. Never, or “Always No,” is sufficient to answer a Yes/No DS question, so the answer is (B), 2) alone is sufficient.
Many students will try to “save time” by skipping straight to the statements, but that’s counterproductive. Take the time to ask yourself if there is a better way to express the information presented to you in the question stem. Doing so can pay the time back twofold if it makes the statements easier to analyze.
~Guest Author, Eli Meyer