The GMAT is an exam that primarily tests your use of logic. One of the most consistent methods used to evaluate your use in logic is to take away your calculator and ask you “difficult” math questions. More specifically, questions that seem really difficult, but break down to simple concepts once you understand what is actually happening.
Of course, giving you all the time in the world to break through the confusion would be counterproductive, because then there’d be no way to differentiate between those who understand concepts and those who use brute force to simply try every possible combination of answer choices (think of MacGruber as someone who wastes a lot of time solving problems).
The questions on the quantitative section of the GMAT often appear very complicated and daunting, but can usually be solved quickly using a little logic. Of course, since the exam can potentially ask you hundreds of different questions, you can’t reasonably memorize every type of trick that can be thrown at you. You can, however, identify some recurring themes that appear frequently and understand why they are tricky. On test day, you still have to apply logic on a case by case basis, but some overarching themes are definitely more prevalent than others.
One such theme used frequently is that of turning a math problem into a story that you have to interpret. Today I want to talk about the compound interest problem. This type of problem is common in finance, but most financiers simply input the arguments into their calculators (or abaci) and spit out a solution. The compound interest situation presented is simply a layering mechanism designed to make the underlying exponent problem harder to see. Breaking through the prose of the question and seeing the fundamental problem for what it is can be the difference between a 1-minute solution and a 4-minute solution.
Let’s look at a compound interest problem that highlights the nature of these questions:
A bank offers an interest of 5% per annum compounded annually on all of its deposits. If 10,000$ is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
(B) 625 : 3125
(C) 100 : 105
(D) 1004 : 1005
(E) 725 : 3225
The first thing to note about this question is that it’s asking about a ratio, which means that the 10,000$ sum will be irrelevant. If you’d put in 100$ instead, or 359$, the ratio would still be the same. The correct answer will therefore not be related to 10,000$ in any way, but it’s also important to try and understand the question being asked before answering in order to avoid getting the right answer to the wrong question.
So what exactly is this question asking? What is the ratio of the interest earned in year 4 to the interest in year 5? This can lead us to some tedious calculations if we’re not careful. We start off with 100$ (or 10,000$, it doesn’t matter). At the end of the first year, we’ll have 5% more, so 105$. I could calculate it for year 2 as well, taking 105$ and multiplying by 1.05. This might take 20 seconds on paper, but will (hopefully) yield a result of 110.25$ I could go through years 3, 4 and 5 to get the respective answers (115.76$, 121.55$ and 127.63$), but that would take a while to calculate by hand.
Moreover, let’s say I have these 5 values; I am now tasked with finding the difference between year 4 and year 5. So now I need to calculate 127.63 / 121.55. Without a calculator… If you get to this point on the exam, you either spend more time trying to figure out the ratio, or you take an educated guess and move to the next question in frustration. Neither of these options is particularly good, so let’s backtrack to see where we veered off the path.
To calculate year one to year two, I took the initial arbitrary amount and multiplied it by 1.05. This is due to the interest compounding annually. The second year, I took the amount after year one and multiplied it by… 1.05 again! Eureka! Now, the pattern emerges. Every year, I take whatever the previous year was, and multiply it by 1.05. This means that, from year n to year n+1, the change will always just be 1.05, or a 5% increase.
Looking over the answers, answer choice C succinctly displays a 5% growth rate, taking whatever 100% of the previous year was and adding on 5%. This will be the correct answer for the growth rate from year one to two, as well as from year four to five. The question would have been much easier had the question been about years one and two, but the GMAT purposefully makes questions more difficult in order to differentiate between those who can identify the pattern and those who try to do each possibly calculation on paper.
On the GMAT, the correct answer can often be achieved by applying a brute force strategy. However, in business, you are rewarded for understanding the underlying concept and not wasting everyone’s time with meandering trial and error experiments. Understanding a concept such as this one about compound interest won’t single-handedly allow you to ace the exam. However, knowing that the exam is trying to appraise your ability to use logic to solve problems should incentivize you to look for the causal logic rather than to undertake tedious calculations.
Remember, there are computers, calculators and smart phones that complete routine computations in seconds. The GMAT is your opportunity to demonstrate not only that you can solve the question, but that you truly understand the question.
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.