If you’ve been studying for the GMAT, you’ve inevitably found yourself in a situation where you were thinking “If only I had a calculator!” Many of my students express this sentiment, especially when doing weird digits questions or when forced to evaluate seemingly impossible percentages or fractions. I’m going to say here what I tell all my students: If you’re bemoaning the lack of access to a calculator, then you’re not viewing the test from the right perspective. The GMAT test-takers are not concerned with your ability to do long division or to multiply really big numbers really quickly. In the real world, you’ll have a calculator for those things. What the test-makers are concerned with is your ability to get the answer to a question in the fastest, most efficient way possible and to detect shortcuts in situations where it would appear no shortcut exists. Thus, when you’re confronted with a situation that seems to require the use of a calculator, you need to take a step back and tell yourself the following: “OK, this question would be easy if I had a calculator. But I don’t have one. So there MUST be some faster, conceptual approach to get to the answer.”
To understand what I mean, let’s take a look at a question that gives most students fits:
What is the sum of the digits of 1029 – 6?
Ok, so this doesn’t look fun. Obviously, if we had a calculator, we could solve this pretty quickly and without much thought. But we don’t have a calculator, so there should be a way to answer this in 2 minutes. Well, one approach is to do the subtraction. We can list out all those zeros and do the long subtraction that we learned in third grade, but there are a lot of zeros in 1029 , and writing them all out and doing the math would definitely take longer than 2 minutes. Well, maybe all those zeros is the issue. Maybe we can simplify this question by seeing what would happen if we just did 101 – 6. In that case, we’d get 4. What if we do 102 – 6? In that case we get 94. And 103 – 6? Here, we get 994. Hmm, looks like there’s a pattern. For every power of 10, we’ll have one fewer 9. When our exponent is 1, we have zero 9s and one 4. When our exponent is 2, we have one 9 and one 4. When our exponent is 3, we have two 9s and one 4. It would thus be reasonable to deduce that if our exponent is 29, we’ll have 28 9s and one 4. In other words, this number will come out to: 999….4, where we have 28 9s followed by a 4 in the units digit.
Well, adding up the sum of those digits is not AS BAD to calculate. Still not fun, but definitely manageable. Now, we just need to do 28(9) + 4. And notice there’s a quick way to do 28(9)! 30(9) is 270. 28(9) has two fewer 9s. So just do 30(9) – 2(9). That’s 270 – 18 = 252. Add the 4 and you get 256.
Now, you might be thinking that the approach outlined above is all well and good on this question, but that there’s no way it’ll come in handy on test day. In a way, you’re right. Chances are very slim that you’ll see this exact question when you take the GMAT. But the actual reasoning process we went through to arrive at the above answer can and should be replicated across many different question-types. To do well on the GMAT, you’ll need to quickly and efficiently identify patterns that will get you to the heart of whatever question is being asked. In many situations, it might appear that you have long and tedious calculations ahead of you. But before diving headfirst into those calculations, take a step back and ask yourself what TRULY makes the question difficult and whether you can find a pattern or shortcut that will enable you to avoid those calculations and save precious time for other questions on the exam.Read More