The GMAT Tip of the Week is a weekly column that includes advice on taking the Graduate Management Admission Test, which is required for admission to most business schools. Every week an instructor from a top test-prep company will share suggestions for improving your GMAT score. This week’s tip comes from Brian Galvin, director of academic programs at Veritas Prep.
The GMAT is a test on which the most complex problems often have the simplest solutions, at least for those willing to reason through them. Students often chase the “hardest” content items available on the test and breeze past—or overlook entirely—the most useful items. Let’s take a look at how some of the GMAT’s trickiest-looking problems lend themselves to simple solutions.
What is the sum of the digits of integer k, if k = (1040 – 46)
While this may look like a monster problem, it is just an arithmetic question. Yes, 1040 is an insanely large number, but conceptually it is not much different from 103 (i.e. 1,000). If you test this relationship with a few small numbers, you can get a good look at what k will look like. For example:
102 – 46 = 100 – 46 = 54
103 – 46 = 1,000 – 46 = 954
104 – 46 = 10,000 – 46 = 9,954
Do you see the pattern? Every time we add one to the exponent, we add another 9 to the solution. And the number of digits in the solution is always the same as the exponent itself. So for this problem, where the exponent is 40, k will have 40 digits: a 5, a 4, and the other 38 are 9s. And since 5 + 4 = 9, then really we’re just adding up 39 9s. And 39*9 is 351 (or you can just see that it will end in a 1, and only A matches).
“Special” math skills are infrequently required or rewarded on the GMAT. Sound fundamentals in arithmetic, algebra, and a few conceptual rules of geometry, probability, and statistics are generally all you need, provided you supplement them with reasoning and ingenuity.
Brian Galvin has been with Veritas Prep since 2006 and has since devoted himself to developing new and better ways to help students master the GMAT. He earned a 99th percentile score on the GMAT and has a bachelor’s degree and a master’s in education from the University of Michigan. He has taught high school history in Detroit, worked in sales and marketing for the Detroit Pistons NBA franchise, and completed an Ironman race.