How to Free Yourself from Calculator Math

There are few things more alluring than shortcuts. Oftentimes we’re aware of how much work, effort or time is required to accomplish a task, but we naturally gravitate towards something that can accomplish that task faster. From buying readymade rice to taking elevators to go up two floors, we’re drawn to things that make our lives even a modicum simpler (including dictionaries). This is why so many people are disappointed when they first learn that the calculator is not allowed on the GMAT.

From the time we’re in elementary school, we’re encouraged to use our calculators to solve even the most mundane equations. If John is buying six dozen eggs, how many total eggs is John buying? Many people instinctively reach for their calculators, even if they can do the simple multiplication in their heads. Calculators provide safety and accuracy. The little machine says that the answer is 72; I won’t even bother double checking the result manually because I know the machine won’t make a mistake. This is even more prevalent as the math involved gets harder (a dozen dozen eggs?). Indeed the lure of the calculator is very strong.

Why does the GMAT not allow for calculators on the exam? Quite simply, the exam is trying to test how you think, not how quickly you can type on a calculator. This allows for questions to include relatively simple math that you must solve manually, or for rather difficult math that you must understand in order to reach a conclusion. Both types of questions show up on the exam, but the answer choices always provide some sort of hint as to what to do, since the correct answer must be among the five choices given.

Let’s look at two simple interest rate questions to highlight the methods we can free ourselves of our calculator addiction:

Marc deposited $8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marc’s account one year after the account was opened?

(A)   8,200

(B)   8,205

(C)   8,400

(D)   8,405

(E)    8,500

Many students (especially those in finance) immediately recognize this as a compound interest problem, which can be solved effortlessly with a financial calculator. You only have to plug in the term, the interest rate, the principal and the rate of compounding, and the calculator will spit out the correct output in a matter of seconds. However, the underlying concept is what the GMAT is really testing. The authors of this question want to ensure you comprehend how to make the calculations, so the question is asking about only one year.

In this case, we can easily calculate the amount without a calculator. We have 8,000$ making 5% annually, which translates to 400$ in one year. Thus, if the interest were compounded annually, the answer would be 8,400$. If we don’t notice that the interest is compounded more frequently than that (or we don’t understand what that entails), then we might pick answer choice C and move on. However, that would be incorrect because the question indicates that the interest is compounded twice a year.

If the interest is compounded twice a year, that means that after 6 months you make 2.5% of the 8,000$, or half of the 400$ we’d previously calculated. If you’re trying to calculate 2.5%, it’s easiest to take 10% and then divide it by four. Multiplying by fractions can be tedious without a calculator, but GMAT questions are set up in such a way that the answers are almost always integers. You just have to determine the best way of getting to that integer without getting bogged down in tedious math.

Whichever method you used, you should have 8,200$ after 6 months. After another 6 months, you need to calculate another 2.5% on 8,200$. The simplest way to do this is to recognize that the 8,000$ will still yield 200$, and only the extra 200$ must be adjusted for. Since we need ¼ of 10%, that’s ¼ of 20$ or exactly 5$. The interest accrued in the second semester will be 205$ instead of simply $200 (#winning), making the total for the year 405$. The correct selection is thus answer choice D.

However, we don’t even need to get this precise on most GMAT questions. Look at the answer choices again. Once we’ve determined that we need slightly more than 400$ in interest because of the compounding, the only answer choice that makes any sense is D. Oftentimes the simple fact that the answer must be slightly higher or lower than a known benchmark eliminates all answer choices except for one. The complete calculations can be accomplished, but a rough estimate will work in 99% of cases.

Let’s look at a similar question where the estimation is our best approach:

Michelle deposited a certain sum of money in a savings account on July 1st, 2012. She earns an 8% annual interest compounded semi-annually. The sum of money in the account on January 1st, 2015 will be approximately what percent of the initial deposit?

(A)   117%

(B)   120%

(C)   121%

(D)   135%

(E)    140%

In this case estimation is the best approach because the answer choices are far apart. If Michelle is earning 8% per year compounded semi-annually, then every six months she’s making about 4%, which over 30 months is 20%. Answer choice B is thus close but ultimately too low for the compounding interest. It must be ever so slightly higher than that, which leads us inexorably to answer choice C. We need a little more than 120%, but there’s no way we can get to 135%. The answer must be C, and we don’t really need to do any verification to know that this is the correct answer (you can do the math and get to 121.67% if you’d like).

While the calculator is an ever-present tool in the real world, the GMAT remains a test designed to test how you think. The shortcuts and instruments you use in everyday life should only serve to accelerate your calculations, not replace the thought processes that allow you make calculations. Remember that if everything you do can be replaced by a calculator (or spreadsheet or abacus), then sooner or later you might be too.

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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.