GMAT Tips for Quant: Problem Solving

What’s your favorite holiday? Christmas? Easter? No matter what your choice is, the favorite of the authors of the GMAT’s problem solving (PS) section is clear: Halloween. And no, that’s not because it’s a scary task to try and answer these monsters’ questions – they must love October 31st because they love dressing up their questions in a ‘costume’. Each question is written in a way to disguise its true objective; in their math concept guide, Lighthouse Review explains: “Solving word problems once they’re set up is usually a breeze. The key to setting up word problems is the proper translation of words and phrases into algebraic symbols.”

Why make it too easy? After all, the GMAT is a test of critical thinking and not, in this case, 8th grade level math. To achieve this outcome, the authors of the test use their best Halloween tricks to confuse the test taker. Luckily for us, we’ve got some tricks too. Keeping with the theme, consider these GMAT tips our equivalent of the Ghostbusters’ ‘proton pack’. They are, as follows:

Backsolving

• Using the answer choices to test if they’re the correct answer. For example, if the question is “What’s X if 2x = 8?” And there’s answer choice of 3, you know that isn’t the correct answer. If there’s an answer choice of 4, however, you know it is correct.

Picking Numbers

• Using numbers – positive, negative, whole, fractions, etc. - to estimate what the correct answer is. For example, if the question is, “What’s the remainder of a prime number greater than 3, divided by 12?” you could pick 5, or any prime number greater than 3, and would determine that the remainder is 1.

These GMAT tips are essential parts of data sufficiency (DS) strategy, as well. But DS requires an additional layer of strategy. For that reason, and because problem solving looks similar to the word problems we all encountered in high school, problem solving is a good place to start. These GMAT tips will explain what your mindset towards PS should be, how to practice, and how to review completed practice problems.

Much like how in American football the quarterback reads the pre-snap defense, when a problem solving problem appears in your studies or on the exam, survey the landscape. Read the prompt and ask yourself, “What are they asking me to do?” At this point, it may also be helpful to glance at the answer choices to gather more information on the problem’s objective.

Once you understand what the problem wants you to do, ask yourself, “What’s the best way to get the answer?” Remember, for quant problems, you’re tasked with answering 37 questions in 75 minutes – about two minutes a question. Since time is scarce and the GMAT doesn’t care how you get the right answer – only that it’s right – you have a few options:

• You can work the problem straight through with brute force
• You can work the problem with a mathematical shortcut
• You can use strategy: backsolving or picking numbers
• You can use the process of elimination to make an informed guess

For example: Sarah’s grade in biology is the average score of five tests. On the first four, she averaged 78%. What does Sarah need to score on the fifth to receive a final grade of 80%?

a) 78%

b) 80%

c) 82%

d) 86%

e) 88%

Again, there are several approaches one can take to this problem. If the math is simple enough - that is, it’s simple enough that you can find the answer in two minutes or less - you could answer it with brute force:

• [(78 x 4) + X] / 5 = 80. Solve for X, resulting in X = 88.

If you know the ‘over/under’ shortcut when working with averages, you can deploy that and find the correct answer in seconds:

• To find the missing number that will result in an average of a string of numbers, count how many times the numbers are ‘over/under’ the desired average and then add that to the desired average. That’s the missing number.
• For this problem, 78% is 2% under 80%; times four test scores makes it a total of 8% ‘under’. That, plus the desired average, 80%, makes the answer 88%. Combined, that makes an average of 80%: answer choice e!

If you aren’t sure of a shortcut and the math is difficult enough that you don’t think you’ll have time to use brute force, you can use a strategic tool like backsolving or picking numbers:

• Because one of the answer choices is the correct fifth score, this is a situation where backsolving is more applicable than picking numbers. In that case, it’s important to know that the GMAT commonly puts the correct answer for these types of questions towards the rear of the answer choices. For that reason, always backsolve from e to a.
• By doing so, you result with an 80% average by inserting 88% into the equation. Answer choice e is correct.

Lastly, if you’re stumped or don’t know where to begin, don’t spin your wheels. Use process of elimination (POE) and common sense to make an informed guess:

• You can use process of elimination to determine that the answer can’t be anything 80% or lower. Logically, it’s got to be something on the upper range of the spectrum - either 86% or 88%. By using process of elimination, you’ve increased your odds from a 20% chance to 50%.