One common complaint I hear from GMAT students is: “I can get the right answer but it takes me too much time.” Many people preparing for the GMAT feel this way at one point or another during their preparation. While this complaint has some merit, it can usually be paraphrased as “I’m approaching the problem with little to no strategy.” Relying on brute force to get the right answer is rarely the best approach. The old adage states that a million monkeys writing on a million typewriters will eventually produce the greatest novel of all time (It was the best of times, it was the blurst of times…).
This problem speaks to the inherent time management skill required to succeed on the GMAT. Almost any question you will face on test day can be solved with a brute force approach. However, you won’t have a calculator and you will be under constant time pressure to complete each question fairly quickly, so simply running through every possible numerical combination seems like a fool’s errand. There may be a time when the brute force approach works, but it is like trying to break into someone’s e-mail by trying 00000001, 00000002, 00000003, etc until you find the correct password. You’d probably have more success with a logical approach (such as guessing birthdays or other important dates) than with trying every possible permutation until the lock opens.
Approaching the problem in a logical and methodical way should be your goal for both quant and verbal questions. The approach as such may vary a little, but pattern recognition and extrapolation are two skills that will come up over and over again. If you’ve ever asked a 5-year-old what 2 + 2 was, they generally answer 4. If you ask them what 1,002 + 1,002 was, you’d usually get a lot of blank stares and puzzled looks. (My attempts to explain that they are essentially the same question have led to more crying fits than I’d care to admit). The GMAT uses the same elements of misdirection to bait you into thinking this particular problem is one that you can’t solve.
Let’s look at a quant problem to get an idea of what we’re looking to do on these questions:
How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?
This is the type of question that most people can get with unlimited time. You can simply go through every possible number from 1 to 249 and see if each number meets the criteria. Apart from going cross-eyed halfway through, you will also spend an atrocious amount of time on a question clearly designed to reward you for using logic. Let’s look at this question logically and see what we can determine.
Firstly, it only cares about positive integers, so we can disregard zero. This is helpful because a lot of questions hinge on whether or not zero is included, but that won’t matter in this instance. Furthermore, only integers matter, and we’re looking for multiples of 4 but not 6. Your initial pass on a question like this might look might concentrate on the multiples of 4 and you might write (part of) the following sequence down:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100…
After writing a couple of dozen numbers, you may try to figure out the pattern and extrapolate from there. Numbers divisible by 6 are to be eliminated, so you could rewrite this sequence:
4, 8, 16, 20, 28, 32, 40, 44, 52, 56, 64, 68, 76, 80, 88, 92, 100…
Even with this, we have a long sequence of numbers, some of which are crossed off, and less than halfway through the entire sequence. Perhaps approaching the question from a more strategic approach would yield dividends:
The number must be divisible by 4 but not by 6. Calculating the LCM gives us 12, which means that every 12th number will be divisible by both of these numbers. We want the integers to be divisible by four, but not by six, so 12 is out. Along the way, we stop by 4 and 8, both of which are divisible by four but not by six. So every 12 numbers, our count goes up by two, and we start the pattern again. 1-12 will give two numbers that work. 13-24 will give two more numbers that work. 25-36 gives two more, 37-48 gives two more and 49-60 gives two more as well. Thus, through 60 numbers, we have 10 elements that are divisible by 4 and not 6.
From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 42, as all the other choices are very far away. The numbers 244 and 248 will come and complete the list that’s (naughty or nice) under 250. Answer choice C is correct here.
There are other ways to get the right answer, but the fastest ones all hinge on pattern recognition. Figuring out that every 12 numbers gives two more answers can take us from 1 to 240 in one shot (20 sequences x 2). Alternatively, once finding 4 elements at 24, you can probably easily envision multiplying the total by 10 and getting to 240 straight away (like warping over worlds in Super Mario Bros).
Timing is one of the key elements being tested on the GMAT, and one of the goals of the exam is to reward those who have good time management skills. Given 10 minutes, almost everyone would get the correct answer to this question, but the exam wants to determine who can get it right in a fraction of that time. On the GMAT, as in business, timing is everything.
Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.