A Pattern of Efficiency
(This is one of a series of GMAT tips that we offer on our blog.)
A colleague recently pointed out a practice test problem he had seen that appeared to be a unique, new variety of GMAT quantitative problem. (Editor’s note: There is no need for alarm; continue reading and you’ll learn that this problem is entirely common on the exam and has been for years!) The problem asked for the test taker to sum a relatively high number of values that were displayed on a grid; the extent of the problem was similar to:
What is the sum of:
-1 + 2 – 3 + 4 – 5 + 6 – 7 + 8 – 9 + 10 – 11 + 12 – 13 + 14 – 15 + 16
Displayed in grid form, the problem in question contained a greater number of values and was asked in a slightly different way, but the takeaway is the same: The GMAT likes to ask questions that seem to require a time-consuming calculation, but can actually be solved relatively quickly through pattern recognition, leading to simpler math.
In this case, each pair of odd-then-even values sums to 1. (-1 + 2), (-3 + 4), etc. will each produce a sum of 1, meaning that the test-taker only need to recognize that pattern, determine the number of pairs* that exist in the sequence (in this case, 8), and multiply the sum of each pair by the number of pairs (1 * 8) to achieve the answer, 8.
The takeaway? When problems look to require extensive calculation, or when you detect that a pattern may be present, look to find a pattern that can make the solution quick and efficient. The GMAT rewards that style of thinking more often than not.
(*Note: be sure in this case to determine whether the sequence does, indeed, contain only distinct pairs; to make the question more difficult, the sequence could end with -17, in which case that value wouldn’t have a complementary positive number, and would have to be subtracted entirely.)
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