Today’s GMAT tip comes from our friends at Veritas Prep. In today’s article, they present the sixth installment of their “Think Like the Testmaker Series,” which focuses this week on solving quantitative questions in an efficient manner:
Brian Galvin is the Director of Academic Programs at Veritas Prep, where he oversees all of the company’s GMAT prep courses.
At graduate school functions, a common elitist quip from engineers and scientists when talking to MBA students is to ask, “Are you majoring in PowerPoint, or Excel?” (A similarly-popular retort is “I’m majoring in outsourcing your job”) While, obviously, business school curriculum is much more substantive than some graduate counterparts will like to admit, the truth does remain that you will use programs like Microsoft Excel quite often in business school, and you’ll also need to buy a fairly sophisticated financial calculator. So, knowing that, why would the GMAT not allow you to use a calculator or spreadsheet device on its quantitative section?
The reason that the GMAT prohibits calculators is that its primary concern is not to test your ability to “crunch numbers,” but rather to assess your ability to problem solve using numbers. In fact, in many cases, questions are crafted in an attempt to bait you in to an attempt to calculate numbers by hand that will be a sufficient combination of time-consuming and error-prone to cripple your test performance and elicit an incorrect answer.
Knowing that the GMAT isn’t a math skills test, but rather a test of problem solving, efficiency, and other, more business-oriented skills and traits, you should prepare yourself to recognize when problems can be solved in a simpler way. Often times, this can be done by recognizing patterns in the ways that numbers interact. Consider the question:
What is the units digit of 225 – 67?
In seeing this question, you may well think that, although it may take some time, you can work through the calculations and actually determine the values of the two exponential terms. After all:
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
46 = 64
And so on. How much more work can it be to get to the 25th power? Well, as the numbers get bigger, you’ll undoubtedly slow down in calculating them — 128, 256, 512, 1024, 2048, 4096, 8192, and that only gets us to the 13th power with the real heavy lifting still to come. If you’ve noticed from the question, however, that the question specifically and exclusively asks for the units digit — the last digit before the decimal point — then you can eliminate most of the work. You don’t need to calculate that 25 = 32, as long as you know that 25 yields a units digit of 2. Multiply by 2, and you’ll know that 26 yields a 4, 27 yields an 8, etc.
What’s more, you can also begin to notice that a pattern emerges, as there is a cycle: 2, 4, 8, 6, 2, 4, 8, 6… The cycle repeats every fourth digit, with the fourth unique digit in the sequence being 6. Therefore, the result for each exponent that is a multiple of four is 6, so 224 will yield a 6. 225 is the next term in the cycle, so the units digit will be 2.
Sixes are easier : 61 = 6; 62 = 36; 63 = 216… This pattern dictates that multiplying a units digit of 6 by 6 is going to yield a 6, so regardless of the exponent (as long as it’s a positive integer) the units digit will be a 6, and you don’t really have to do any math.
One last twist to this problem: you need to realize that 225 will be considerably larger than 67, so your subtraction problem will look something like:
XXXXXXXXXXX2
– YYYYYYYY6
The answer, then, is 6, as this problem will take the form of 12-6 (since this multiple of 2 is clearly larger than this multiple of 6), and not of 2-6 (yielding -4), which would be the case if the 2 term were known to be smaller than the 6 term.
Again, the GMAT is testing something a little higher-order than math here — did you consider all of the possibilities, or make a quick, incorrect assumption when you thought you were done?
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