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Posted on
07
Jul 2020

GMAT Problem – Speed Distance Problem

Speed and distance problems are among the most complained about problems on the GMAT. Numerous clients come to us and say they have difficulty with speed and distance problems, word problems, or work rate problems. So we’re going to look at a particularly difficult one and see just how easy it can be with the right approach.

The Two Cars Problem

In this problem we have two cars – car ‘A’ and ‘B’. Car ‘A’ begins 20 miles behind car ‘B’ and needs to catch up. Our immediate DSM (Default Solving Mechanism) is to dive in and create an equation for this and that’s exactly what we don’t want to do.

These types of problems are notorious for being algebraically complex, while conceptually simple. If you hold on to the algebra, rather than getting rid of it, you’re going to have a hard time.

Solution Paths

In this problem we’re going to build up solution paths. We’re gonna skip the algebra entirely. We’re going to take a look at an iterative way to get to the answer and then do a conceptual scenario, where we literally put ourselves in the driver’s seat to understand how this problem works. So if we want to take the iterative process we can simply drive the process hour-by-hour until we get to the answer.

Iterative solution path

We can imagine this on a number line or just do it in a chart with numbers. ‘A’ starts 20 miles behind ‘B’ so let’s say ‘A’ starts at mile marker zero. ‘B’ starts at 20. After one hour ‘A’ is at 58, ‘B’ is at 70 and the differential is now -12 and not -20. After the second hour ‘A’ is at 116, ‘B’ is at 120. ‘A’ is just four behind ‘B’. After the third hour ‘A’ has caught up! Now it’s 4 miles ahead. At the fourth hour it’s not only caught up but it’s actually +12, so we’ve gone too far. We can see that the correct answer is between three and four and our answer is three and a half.

Now let’s take a look at this at a higher level. If we take a look at what we’ve just done we can notice a pattern with the catching up: -20 to -12 to -4 to +4. We’re catching up by 8 miles per hour. And if you’re self-prepping and don’t know what to do with this information, this is exactly the pattern that you want to hinge on in order to find a better solution path.

You can also observe (and this is how you want to do it on the exam) that if ‘A’ is going 8 miles an hour faster than ‘B’, then it’s catching up by 8 miles per hour. What we care about here is the rate of catching up, not the actual speed. The 50 and 58 are no different than 20 and 28 or a million and a million and eight. That is, the speed doesn’t matter. Only the relative distance between the cars and that it changes at 8 miles per hour.

Now the question becomes starkly simple. We want to catch up 20 miles and then exceed 8 miles, so we want to have a 28 mile shift and we’re doing so at 8 miles an hour. 28 divided by 8 is 3.5.

Conceptual scenario solution path

You might ask yourself what to do if you are unable to see those details. The hallmark of good scenarios is making them personal. Imagine you’re driving and your friend is in the car in front of you. He’s 20 miles away. You guys are both driving and you’re trying to catch up. If you drive at the same speed as him you’re never going to get there. If you drive one mile per hour faster than him you’ll catch up by a mile each hour. It would take you 20 hours to catch up. This framework of imagining yourself driving and your friend in the other car, or even two people walking down the street, is all it takes to demystify this problem. Make it personal and the scenarios will take you there.

Thanks for the time! For other solutions to GMAT problems and general advice for the exam check out the links below. Hope this helped and good luck!

Found it helpful? Try your hand at some other GMAT problems: Profit & Loss Problem.


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Posted on
11
Jun 2020

Snack Shop GMAT Problem

The Snack shop GMAT problem is an average or a mean problem. A characteristic of many average problems is that one big takeaway right at the outset is that the answer choices are clustered tightly together. We want to refrain from making any calculations.

The problem is below:

snack shop problem

Selecting A Solution Path

If they’re looking for a level of precision, the estimation solution path isn’t available to us. If we dive into the problem, right from the first sentence we have sort of a conclusion that we can create via either a graphic or accounting solution path.

If you were the business owner immediately you’d say to yourself: Well for 10 days and an average of $400 a day I made $4000. 

This is how we want to think about averages. Many times they’ll tell us a parameter about a length of time or over a certain universe of instances and here we want to treat them all as equal.

Solving the Problem

It doesn’t matter if one day we made 420 and another day we made 380. We can treat them in aggregate as all equal and start out with that assumption. That’s a very useful assumption to make on average problems. So, we start out knowing that we made 4,000. 

What I want us to do is do a little pivot and notice from a running count standpoint how much above or below we are on a given day. So we’re told that for the first six days we averaged $360 which means each of those six days we’re short $40 from our average. That means in aggregate we’re short $240. 6 days times $40 –  and this has to be made up in the last 4 days.

Notice how we’re driving this problem with the story rather than with an equation. In the last four days we need to outperform our 400 by 240. 240 divided by 4 is 60. 60 on top of the 400 target 

that we already have is 460. Therefore, our answer is D.

Graphical Solution Path

If we are more comfortable with graphic solution paths, imagine this in terms of 10 bars each representing $400. Lowering six of those bars down by 40 and taking the amount that we push those first six down and distributing it among the last four bars gives us our $460 total per day.

snack shop graphic solution path

If you enjoyed this Snack Shop GMAT Problem, watch “The Gas Mileage GMAT Problem” next.

 

 

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Posted on
28
May 2020

Gas Mileage GMAT Problem

The Gas Mileage problem is a classic example of the GMAT triggering one of our DSM’s: Our Default Solving Mechanisms for applied math. Yet there are three higher level solution paths that we can engage instead. So we are going to skip the math entirely on this one. In reading the question stimulus, there’s a signal that estimation is going to be a very strong and viable solution path and in fact for most folks estimation is the dominant solution path for this problem.

What to Take Note Of

Notice in the first sentence here that we are given the relationship between the efficiency for Car X and the efficiency for Car Y. When comparing 25 to 11.9, 11.9 is a little bit less than half. Whenever we have a relationship that is a little less or a little more than a factor, that’s a clear signal that the GMAT wants us to estimate.

Now, we have an inverse relationship here, between the efficiency of Cars X and Y and the amount of gas they use. So if Car Y is using a little half or rather if Car Y has a little less than half efficiency it’s going to use a little more than double the amount of gas. Managing the directionality of estimation is essential to make full use of this solution path.

Estimation Solution Path

Right off the bat, we have a sense that Car Y is going to use a little bit more than double the amount of gas. Now, all we need to do is figure out how much Car X will use. This is an exercise in mental math. Instead of dividing the 12,000 miles by 25 we want to build up from the 25 to 12,000.

Ask ourselves, in a scenario type of way, how many 25’s go into 100 – The answer is 4. 4 quarters to a $1. Then we can scale it up just by throwing some zeros on. So, 40 25’s are 1,000. How do we get from 1,000 to 12,000? We multiply by 12. So 40 times 12, 480 25’s gives us our 12,000 miles. Car X uses 480 gallons.

Therefore, Car Y is going to use a little more than double this and we point to answer C because we just need to answer the amount Y uses in addition to X. SO there is a bit of verbal play there that we also have to recognize. That’s the estimation solution path.

Graphical Solution Path

We can see this via the graphic solution path by imaging a rectangle, where we have the efficiency of the engine on one side and the amount of gallons on the other. With Car X, 25 miles per gallon time 480 gallons is going to give us the area of 12,000 miles. That is we’ve driven the 12,000 miles in that rectangle. If we are cutting it in half on efficiency, or a little more than half, we end up with two strips and if we lay them side by side we see that we’re doubling of going a little more than double on the amount of gas that we use to maintain that 12,000 mile area.

Logical Solution Path

Finally, we can look at this from a logical solution path which overlaps a bit with the estimation. But the moment we know that Y uses a little more than double the amount of gas of X, we can also look at and not manage that directionality and just say it uses about double. The only answer choice among our answer choices that is close but not exactly, is C – 520. 480 is our exact number and the A answer is way too low. It’s not close enough to 480 to be viable. So here is an example where, while best practices have us managing the directionality, we don’t even need to do that.

Similar Problems

For similar problems like this take a look at the Wholesale Tool problem, The Glucose Solution Problem and for a really good treatment of the graphic solution path check out Don’s Repair Job. There should be links to all three right below and I hope that this helps you guys on your way to achieving success on the GMAT.

If you enjoyed this Gas Mileage Problem but would like to watch more videos about Meta strategy, try “How coffee affects your GMAT performance”.

 

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Posted on
22
May 2020

Percentage GMAT Problem

Mike is here with your Apex GMAT problem of the day. Today we are going to look at a percentage problem and we are going to break it down based upon a few characteristics. This is a very typical GMAT percentage problem.

Approximately

So, first things first, the thing that you should hone in on immediately in this problem is this term “approximately”. Whenever you see the term you know that they’re not going to give you a precise answer, and so you are not on a hook for the precise answer. It should scream estimation to you!

Questions Tricks

If you take a look at the problem itself you see that they offer you two numbers that you will be comparing. But one of the interesting features is that they give you the more complicated, more ugly number, less round number, first and the other number, the 28,000, second. And this is designed to focus you towards the more exacting approach. When in fact, your optimal solution path is recognizing that the 28,000 is your base and instead of computing the differential, super math style, of you know 36,700 minus 28,000 and then putting it over the 28,000, the original number.

What If?

Instead we want to play a “What If” and say okay, 28,000 is my base so what if I took 10% of it? That’s going to be 2,800. What if I took 20% of it? 5,600. What if I took 30% of it? And there’s your number right there. So, what we can see if it’s not immediately apparent from a scale perspective is that this big ugly number here is 30% higher. Even if we had that from the scale perspective. Even if we’ve recognized it’s about a one-third higher.

Notice there are two answer choices that are tightly clustered around that 30 percent. There is the 30% that’s our correct answer. Because the real number is somewhere around 31 percent and change. But there’s also that 28%, and so we need to get to some exacting level.  And we do this by playing that “What If?” and saying: Okay, we can fit three blocks of 2,800 in and that gets us just below the target number that they give us in the problem.

Clustered Answers

This is a great problem to problem form. And you can play around with your mental map as well on it. Also, there’s a signal. It’s more of a subtle one and a little less reliable in the answer choices. On the one hand, you have the cluster of 28 and 30. And so, you can reasonably suggest that because these two numbers are close together and because we’re looking at estimation as a solution path.

The GMAT is testing our differentiation and our estimation skills. And that hones us into, or narrows us down to a B vs. C situation. Other clusters that are here, that are less meaningful is the difference between A and C which is a factor of ten. But given that, and given our B vs. C once again, we are pointed towards a C answer. Now we have two different clusters that share C in common.

The GMAT does this a lot more often than you might think. And while it’s not always 100% reliable, it can be a very valuable tool. Especially when you’re short on time or need to make a decision on a problem where you don’t have a lot of uncertainty.

So, thanks for watching guys! Check out the links for other GMAT Quant & Verbal problems below and I’ll see you guys again soon.

If you enjoyed this Percentage GMAT Problem, try out others: Combinatorics Problem

 

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