Mia Saini: Hi and welcome back to MBA PodTV. I’m your host, Mia Saini.

Today, we’re running through a tricky GMAT math problem with Manhattan GMAT instructor Jonathan Schneider. So take out your pencils and your notebook and get ready.

Jonathan Schneider: Hi! My name is Jonathan Schneider. I am an instructor here with Manhattan GMAT. I scored 780 on the GMAT about two years ago. I’ve been working for Manhattan GMAT for the past two years. I’ve done a lot of our online courses and I also teach in person and do live tutoring here in New York.

I’m going to be leading you on a math problem today. Take a moment and look over this slide, and if you would like to pause it so that you can try the problem on your own, feel free to do so.

Okay. So as you’ll notice here, there are a couple of different ways that we can begin a problem like this. One thing that people will often try to do is approach this with direct algebra, and that’s very possible and it’s a great solution, but you have to know how to manipulate that algebra.

In terms of deciding how to represent this as an equation, we first need to deal with X percent. In terms of working with a variable as a percent, simply think of the word “percent” as meaning over 100. X percent then simply translates to X divided by 100. Of Y percent, the “of” always means multiplication, and we do the same thing where we put Y over 100. From there, we think “of Z” as meaning times Z, and in this way we can begin our translation.

Now, after this point, we have to determine what it means to be reduced by Y percent, and a reduction is very similar to how we would think in terms of day-to-day pricing. This is something that we can all do in our heads. Representing it mathematically with variables is a bit more challenging.

We can try to multiple by 1 minus Y percent and that will capture the decrease of Y percent. The 1 stands in for the original value and the minus Y percent or in this case minus Y over 100 represents the decrease, and that becomes our entire expression.

Now, at this point, we have a very complex expression and it doesn’t match any of our answer choices. So from here, we have to manipulate this a little bit further, and what you’ll see that you probably like to try at first is to combine these denominators into a common form. In doing that, you have to make sure that you combine in such a way that you can take these two parts across the subtraction sign and get them to have the same denominator. That is going to allow us then to combine everything into one simplified expression.

Now, it’s fairly easy to combine on this first slide and you’ll see that you have over 10,000 from the two 100s. Noticing on the second slide though, we have this over 100 three separate times. This is going to give us the denominator of 1,000,000 and we need to create our first fraction in such a way as to agree with that second fraction. We need to, in other words, create the denominator in the first fraction as 1,000,000 also.

In order to do that and to keep the same value, we need to also multiply the numerator of that first fraction by 100, and this is what allows us to get to our final answer where we have a 100 multiplied by the first polynomial in the numerator.

Of course I mentioned that we have an alternate approach here as well. We could pick numbers. Now, in order to do that, we want to be able to pick smart numbers, numbers that are going to work conveniently for this problem. We oftentimes want to approach the problem this way when we have variables in the answer choice. It’s going to allow us a simplified form without having to set up complex algebra.

Now, in order to do this, we want to pick a smart number and we want to start with the number 100, but you have to know what to pick that for because we have three variables here.

In this problem, it’s going to be easiest to pick 100 for Z because Z is the starting value. And then pick other smart numbers for X and for Y. A smart number for Y might be 50 because 50% is simply one-half and that is going to be easy to calculate. We could furthermore take X to be 10 and then we would simply be taking 10% of 50% of 100, and we can do that calculation now quite simply.

Now, after that point, we need to think about what a 50% decrease would mean because again, we have chosen Y as 50. So simply take a 50% decrease of the number that we have reached so far and you’ll see that we end up with a target value.

Now, this target value is something that we can use to look for in our answer choices. All that we need to do is attempt to plug in each of our chosen values into the expressions in the answer choices and see where we come out with a match for our target value. Ideally, we’ll only come out with one match and that will be our answer. Of course sometimes we do hit two or more choices that match, at which point we have to choose new numbers or at least change one of the numbers and try the system again.

Mia Saini: Wow! Working on that GMAT problem gave me flashbacks when I took the GMAT five years ago. So don’t put your notebooks away just yet. We have many more problem-solving exercises from both the quantitative and verbal sections of the GMAT.

Well, that’s it for this edition of MBA PodTV. I’m your host, Mia Saini. Visit us at MBAPodcaster.com to get the latest audio and video shows, and follow us on Facebook and Twitter to get the latest news and insight on your MBA application process.