Handling logic questions in an interview

“It’s a trap! Wait, is it a trap?”

Today we’ll be discussing the topic of logic questions as they pertain to interviews—We’ll look at what they’re for and how they work. Then, we’ll go over how to break them down and respond to them quickly and accurately. Last, we’ll cover how to save yourself if you’re stumped and you can’t find the right answer. By the end of this article, you should feel comfortable breaking down and answering logic questions.

Logic questions—some people call them brain teasers—are a common part of many analytics interviews. These multi-disciplinary, multi-step questions allow a hiring manager to evaluate the ability of the candidate to break down a problem, understand it, and then solve it. They’re also one of the spots where candidates tend to slip up the most, mainly because there are many places you can go wrong when answering one of these questions. For example:

There is a cloth factory with eight machines on the main floor. If four machines working together at a constant rate can produce 100 yards of cloth in two hours—how long would it take to produce 1200 yards of cloth if six of the machines were working together?

Take a minute and try to solve the problem above before reading on. Many people struggle with these types of questions in interviews because in many cases they’re meant to be challenging. Let’s solve the example above together, paying special attention to the methodology used and noting the places you could slip up.

Step 1: Figure out what’s important and what’s not.

This is the first step and also one of the most crucial. Questions like this will sometimes include information that is superfluous—in other words, you don’t need it to solve the problem.

This step is a test to see if you’re able to look at a jumble of information and pick out the pieces relevant to the problem you are trying to solve. Analysts use this skill every day to parse datasets, evaluate conclusions, and even figure out which pieces of information to include in a presentation to management.

You may have noticed that the first line of the question says that there are eight machines on the main floor. The second part tells you how long it takes four machines to produce 100 yards of cloth, and the last part asks how long it would take six  of those machines to make a 1200 yards of cloth.

One of those numbers exists only to confuse you. In reality, the first line is not needed to answer the question, so we can get rid of it. Now we have just the information we need:

If four machines working together at a constant rate can produce 100 yards of cloth in two hours—how long would it take to produce 1200 yards of cloth if six of the machines were working together?

Step 2: Figure out what the question is asking you to do.

This seems obvious, but people tend to skip this step when under pressure. As a result, many people end up not answering the right question.

This part of the question is designed to test whether you’re adequately detail-oriented in your approach to solving a problem. You may know the math but if you answer the wrong question because you weren’t reading carefully, you’ll still fail.

This question is based on the formula D = R*T or “Distance equals rate multiplied by time”. If you’ve already figured that out—good for you, it will come in handy later when we actually  solve the problem, but for now it serves only to illustrate the point that rushing through the details can seriously mess you up:

D = R*T can be rewritten two different ways: T=D/R and R=D/T.

Before your eyes glaze over because math, our point is that there are 3 different variables you could solve for: The number of machines, the number of pounds of cloth produced, and the number of hours it took to produce the cloth. Without looking, which of the variables is the question above asking you to solve for? Do you remember?

In this case, the question is asking you how long, which means we’re solving for time: T = D/R.

Step 3: Figure out which pieces of information you already have.

If you’re comfortable using formulas then you can switch into math mode here, but if not—or if you can’t figure out the formula that relates to the problem—you can still use logic to figure out which pieces of information you have at your disposal. We’ll solve the problem using a combination of the two below:

So if we’re math people, then we already know that the question is asking us for T,  and that T=D/R. Let’s evaluate whether we have the information necessary to solve the problem. We have D—that’s the number of yards of cloth produced—in this case 1200 yards. Do we have R?

This is another spot where people trip up when under pressure: Reading back through the question it seems at first as though we aren’t given the R. However, upon further inspection you may notice that we have been given a rate.

It may not be the R value we need to solve the problem, but we can use it to get the base R value like this:

4 machines produce 100 yards of cloth in 2 hours. How much cloth does 1 machine produce in 1 hour? (This is the base R value).

We don’t actually need to use any formulaic math here, only logic and basic arithmetic:

We know the machines are all working at the same rate, which means that if 4 machines produce 100 yards in 2 hours then those same 4 machines will produce 50 yards of cloth in 1 hour. Divide 50 yards by 4 machines and you get 12.5 yards per machine per hour, which if we’re using formulas can be rewritten like this:

‘1 machine’s rate = 12.5 yards of cloth/1 hour’ = ‘R = D/T’

Now we know that D = 1200 and R = 12.5

This section tests your ability to link seemingly disparate values together to synthesize a new value. It also tests whether you understand that being given a relative value (in this case the rate of production of 4 machines) allows you to derive what you need to answer the question.

Step 4: Plug your values in and solve.

Method 1: The Formula Method

If you know the formula this part is easy:

T = D/R  so T = 1200/12.5 = 96 hours right?

Right, except that’s not what the question was asking you was it? The question was asking how long it would take six machines to produce 1200lbs of cloth—you only have the rate for one, which means there’s a missing variable, N = number of machines working at the same time.

Remember: A good question will give you an opportunity to slip up right at the end. Keep an eye out for last-second tricks.

We know that six machines do six times the work, which means the answer is:

T = 1200/(12.5*6) = 16 hours.

Method 2: Logic Method

If you don’t know the formula or you think better in non-math terms, try turning the formula into a logical sentence and plug the numbers into the sentence like this:

If 4 machines make 200 yards of cloth in 2 hours, and 1 machine makes 12.5 yards of cloth in one hour, then six machines make 75 yards of cloth in one hour. If that is true, then at a rate of 75 yards an hour, it would take ___ hours to make 1200 yards of cloth.

From here it’s pretty easy to tell that 1200/75  will give you the answer:  16 hours.

Conclusion

Let’s recap the steps to solving a logic problem together:

1. Figure out what’s important and what’s not.
2. Figure out what the question is asking you to do.
3. Figure out the pieces of information you already have.
4. Plug your values in and solve.

In an interview, it’s extremely important that you take the time to go through all four of these steps out loud as you solve the problem. As mentioned above, each part of the question is designed to highlight a certain ability or skill.

It’s like showing your work on a math test. By going over the steps out loud, you can actually check every single box and show the hiring manager that not only do you understand how to solve the problem, you also understand why these types of questions are important.

Following this method can save you in the event that you get the question wrong—if you solve the problem silently and blurt out an incorrect answer, the only thing the hiring manager knows is that the answer is wrong. By solving the problem out loud, you have the chance to show the hiring manager your thought process, which can actually save you in the event you get the question wrong.

Lastly, the GMAT exam features these types of questions very heavily. If you’re uncomfortable solving these, just google “sample GMAT questions” and go nuts. The best way to get really good at these types of questions is to drill the methodology over and over again.