Posted on
17
Feb 2021

Data Sufficiency: Area of a Triangle Problem

Hey guys! Today we’re checking out a geometry Data Sufficiency problem asking for the area of a triangle, and while the ask might seem straightforward, it’s very easy to get caught up in the introduced information on this problem. And this is a great example of a way that the GMAT can really dictate your thought processes via suggestion if you’re not really really clear on what it is you’re looking for on DS. So here we’re looking for area but area specifically is a discrete measurement; that is we’re going to need some sort of number to anchor this down: whether it’s the length of sides, or the area of a smaller piece, we need some value!

Begin with Statement #2

Jumping into the introduced information, if we look at number 2, because it seems simpler, we have x = 45 degrees. Now you might be jumping in and saying, well, if x = 45 and we got the 90 degree then we have 45, STOP. Because if you’re doing that you missed what I just said. We need a discrete anchor point. The number of degrees is both relative in the sense that the triangle could be really huge or really small, and doesn’t give us what we need. So immediately we want to say: number 2 is insufficient. Rather than dive in deeply and try and figure out how we can use it, let’s begin just by recognizing its insufficiency. Know that we can go deeper if we need to but not get ourselves worked up and not invest the time until it’s appropriate, until number 1 isn’t sufficient and we need to look at them together.

Consider Statement #1

Number 1 gives us this product BD x AC = 20. Well here, we’re given a discrete value, which is a step in the right direction. Now, what do we need for area? You might say we need a base and a height but that’s not entirely accurate. Our equation, area is 1/2 x base x height, means that we don’t need to know the base and the height individually but rather their product. The key to this problem is noticing in number 1 that they give us this B x H product of 20, which means if we want to plug it into our equation, 1/2 x 20 is 10. Area is 10. Number 1 alone is sufficient. Answer choice A.

Don’t Get Caught Up With “X”

If we don’t recognize this then we get caught up with taking a look at x and what that means and trying to slice and dice this, which is complicated to say the least. And I want you to observe that if we get ourselves worked up about x, then immediately when we look at this BD x AC product, our minds are already in the framework of how to incorporate these two together. Whereas, if we dismiss the x is insufficient and look at this solo, the BD times AC, then we’re much more likely to strike upon that identity. Ideally though, of course, before we jump into the introduced information, we want to say, well, the area of a triangle is 1/2 x base x height. So, if I have not B and H individually, although that will be useful, B x H is enough. And then it’s a question of just saying, well, one’s got what we need – check. One is sufficient. Two doesn’t have what we need – isn’t sufficient, and we’re there. So,

I hope this helped. Look for links to other geometry and fun DS problems below and I’ll see you guys soon. Read this article about Data sufficiency problems and triangles next to get more familiar with this type of GMAT question.

Posted on
11
Feb 2021

Combinatorics: Permutations and Combinations Intro

By: Rich Zwelling, Apex GMAT Instructor
Date: 11th February, 2021

GMAT Combinatorics. It’s a phrase that’s stricken fear in the hearts of many of my students. And it makes sense, because so few of us are taught anything about it growing up. But the good news is that, despite the scary title, what you need to know for GMAT combinatorics problems is actually not terribly complex.

To start, let’s look at one of the most commonly asked questions related to GMAT combinatorics, namely the difference between combinatorics and permutations

Does Order Matter?

It’s important to understand conceptually what makes permutations and combinations differ from one another. Quite simply, it’s whether we care about the order of the elements involved. Let’s look at these concrete examples to make things a little clearer:

Permutations example

Suppose we have five paintings to hang on a wall, and we want to know in how many different ways we can arrange the paintings. It’s the word “arrange” that often gives away that we care about the order in which the paintings appear. Let’s call the paintings A, B, C, D, and E:

ABCDE
ACDEB
BDCEA

Each of the above three is considered distinct in this problem, because the order, and thus the arrangement, changes. This is what defines this situation as a PERMUTATION problem.

Mathematically, how would we answer this question? Well, quite simply, we would consider the number of options we have for each “slot” on the wall. We have five options at the start for the first slot:

_5_  ___ ___ ___ ___

After that painting is in place, there are four remaining that are available for the next slot:

_5_  _4_ ___ ___ ___

From there, the pattern continues until all slots are filled:

_5_  _4_ _3_ _2_ _1_

The final step is to simply multiply these numbers to get 5*4*3*2*1 = 120 arrangements of the five paintings. The quantity 5*4*3*2*1 is also often represented by the exclamation point notation 5!, or 5 factorial. (It’s helpful to memorize factorials up to 6!)

Combinations example

So, what about COMBINATIONS? Obviously if we care about order for permutations, that implies we do NOT care about order for combinations. But what does such a situation look like?

Suppose there’s a local food competition, and I’m told that a group of judges will taste 50 dishes at the competition. A first, a second, and a third prize will be given to the top three dishes, which will then have the honor of competing at the state competition in a few months. I want to know how many possible groups of three dishes out of the original 50 could potentially be selected by the judges to move on to the state competition.

The math here is a little more complicated without a combinatorics formula, but we’re just going to focus on the conceptual element for the moment. How do we know this is a COMBINATION situation instead of a permutation question?

It’s a little tricky, because at first glance, you might consider the first, second, and third prizes and believe that order matters. Suppose that Dish A wins first prize, Dish B wins second prize, and Dish C wins third prize. Call that ABC. Isn’t that a distinct situation from BAC? Or CAB?

Well, that’s where you have to pay very close attention to exactly what the question asks. If we were asking about distinct arrangements of prize winnings, then yes, this would be a permutation question, and we would have to consider ABC apart from BAC apart from CAB, etc.

However, what does the question ask about specifically? It asks about which dishes advance to the state competition? Also notice that the question specifically uses the word “group,” which is often a huge signal for combinations questions. This implies that the total is more important than the individual parts. If we take ABC and switch it to BAC or BCA or ACB, do we end up with a different group of three dishes that advances to the state competition? No. It’s the same COMBINATION of dishes.

Quantitative connection

It’s interesting to note that there will always be fewer combinations than permutations, given a common set of elements. Why? Let’s use the above simple scenario of three elements as an illustration and write out all the possible permutations of ABC. It’s straightforward enough to brute-force this by including two each starting with A, two each starting with B, etc:

ABC
ACB
BAC
BCA
CAB
CBA

But you could also see that there are 3*2*1 = 3! = 6 permutations by using the same method we used for the painting example above. Now, how many combinations does this constitute? Notice they all consist of the same group of three letters, and thus this is actually just one combination. We had to divide the original 6 permutations by 3! to get the correct number of permutations.

Next time, we’ll continue our discussion of permutation math and begin a discussion of the mechanics of combination math.

Posted on
02
Feb 2021

Similar Triangles – GMAT Geometry

By: Rich Zwelling, Apex GMAT Instructor
Date: 2nd February, 2021

One of the most important things to highlight here is that “similar” does not necessarily mean “identical.” Two triangles can be similar without being the same size. For example, take the following:

Even though the triangles are of different size, notice that the angles remain the same. This is what really defines the triangles as similar.

Now, what makes this interesting is that the measurements associated with the triangle increase proportionally. For example, if we were to present a triangle with lengths 3, 5, and 7, and we were to then tell you that a similar triangle existed that was twice as large, the corresponding side lengths of that similar triangle would have to be 6, 10, and 14. (This should be no surprise considering our lesson on multiples of Pythagorean triples, such as 3-4-5 leading to 6-8-10, 9-12-15, etc.)

You can also extend this to Perimeter, as perimeter is another one-dimensional measurement. So, if for example we ask:

A triangle has line segments XY = 6, YZ = 7, and XZ = 9. If Triangle PQR is similar to Triangle XYZ, and PQ = 18, as shown, then what is the perimeter of Triangle PQR?

Answer: Perimeter is a one-dimensional measurement, just as line segments are. As such, since PQ is three times the length of XY, that means the perimeter of Triangle PQR will be three times the perimeter of Triangle XYZ as well. The perimeter of Triangle XYZ is 6+7+9 = 22. We simply multiply that by 3 to get the perimeter of Triangle PQR, which is 66.

Things can get a little more difficult with area, however, as area is a two-dimensional measurement. If I double the length of each side of a triangle, for example, how does this affect the area? Think about it before reading on…

SCENARIO

Suppose we had a triangle that had a base of 20 and a height of 10:

The area would be 20*10 / 2 = 100.

Now, if we double each side of the triangle, what effect does that have on the height? Well, the height is still a one-dimensional measurement (i.e. a line segment), so it also doubles. So the new triangle would have a base of 40 and a height of 20. That would make the area 40*20 / 2 = 400.

Notice that since the original area was 100 and the new area is 400, the area actually quadrupled, even though each side doubled. If the base and height are each multiplied by 2, the area is multiplied by 22. (There’s a connection here to units, since units of area are in square measurements, such as square inches, square meters, or square feet.)

Now, let’s take a look at the following original problem:

Triangle ABC and Triangle DEF are two triangular pens enclosing two separate terrariums. Triangle ABC has side lengths 7 inches, 8 inches, and 10 inches. A beetle is placed along the outer edge of the other terrarium at point D and traverses the entire perimeter once without retracing its path. When finished, it was discovered that the beetle took three times as long as it did traversing the first terrarium traveling at the same average speed in the same manner. What is the total distance, in inches, that the beetle covered between the two terrariums?

A) 25
B) 50
C) 75
D) 100
E) 125

Explanation

This one has a few traps in store. Hopefully you figured out the significance of the beetle taking three times as long to traverse the second terrarium at the same average speed: it’s confirmation that the second terrarium has three times the perimeter of the first. At that point, you can deduce that, since the first terrarium has perimeter 7+8+10 = 25, the second one must have perimeter 25*3 = 75. However, it can be tempting to then choose C, if you don’t read the question closely. Notice the question effectively asks for the perimeters of BOTH terrariums. The correct answer is D.

Posted on
29
Jan 2021

GMAT Data Sufficiency Introduction

By: Apex GMAT
Contributor: Altea Sulollari
Date: 29th January, 2021

As a GMAT test-taker, you are probably familiar with data sufficiency problems. These are one of the two question types that you will come across in the GMAT quant section, and you will find up to 10 of them on the exam. The rest of the 31 questions will be problem-solving questions.

The one thing that all GMAT data-sufficiency questions have in common is their structure. That is what essentially sets them apart from the problem-solving questions.

Keep on reading to find out more about these questions’ particular structures and the topics that they cover:

The question structure:

The GMAT data sufficiency problems have a very particular structure that they follow and that never changes. You are presented with a question and 2 different statements. You will also be given 5 answer choices that remain the same across all data sufficiency problems on the GMAT exam. These answer questions are the following:

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

Your job would be to determine whether the 2 statements that you are provided with are sufficient to answer the question.

What topics are covered?

Some of the math topics that you will see in this type of question are concepts from high school arithmetic, geometry, and algebra.

Below, you’ll find a list of all concepts you need to know for each math topic:

Geometry

• Circles
• Angles
• Lines
• Triangles
• Coordinate geometry
• Polygons
• Surface area
• Volume

Algebra

• Functions
• Equations
• Inequalities
• Exponents
• Algebraic expressions
• Polynomials
• Permutations and combinations

Arithmetic

• Basic statistics
• Real numbers
• Number theory
• Fractions
• Percentages
• Decimals
• Probability
• Integer properties
• Power and root

• Sets
• Profit
• Percentage
• Ratio
• Rate
• Interest
• Mixtures

Common mistakes people make when dealing with this question type

Actually solving the question

This is the #1 mistake most test-takers make with these problems. These problems are not meant to be solved. Instead, you will only need to set up the problem and not execute it. That is also more time-efficient for you and will give you some extra minutes that you can use to solve other questions.

Over-calculating

This relates to the first point we made. This question type requires you to determine whether the data you have is sufficient to solve the problem. In that case, calculating won’t help you determine that. On the contrary, over-calculating will eat up your precious minutes.

Rushing

This is yet another common mistake that almost everyone is guilty of. You will have to spend just enough time reading through the question in order to come up with a solution. Rushing through it won’t help you do that, and you will probably miss out on essential details that would otherwise make your life easier.

Not understanding the facts

What most test-takers fail to consider is that the fact lies in the 2 statements that are included in the questions. Those are the only facts that you have to consider as true and use in your question-solving process.

3+ tips to master this question type:

Review the fundamentals

That is the first step you need to go through before going in for actual practice tests. Knowing that you will encounter these high school math fundamentals in every single quant problem, is enough to convince anyone to review and revise everything beforehand.

This might sound a bit intimidating at first as most answer choices are very long sentences that tend to be similar to each other in content. However, there is a way to make this easier for you. What you need to do is synthesize the answer choices into simpler and more manageable options. That way, they will be easier to remember. This is what we suggest:

1. Only statement 1
2. Only statement 2
3. Both statements together
4. Either statement
5. Neither statement

Examine each statement separately

That is definitely the way to go with this GMAT question. You will need to determine whether one of the statements, both, either, or neither is sufficient, and you cannot do that unless you look at each of them separately first.

Now that you have read the article and are well-aware of the best ways to solve data sufficiency problems on the GMAT, try your hand at this

Posted on
20
Nov 2020

GMAT How-to: Probability Problems

By: Apex GMAT
Contributor: Altea Sulollari
Date: 20th November 2020

GMAT probability questions, which test logical reasoning skills, tend to be quite daunting. The good news is that they don’t appear very frequently; the Quant section contains no more than three or four probability questions. However, since so many test-takers struggle with these questions, mastering probability can be an excellent way to boost your overall score.

GMAT probability questions aren’t so hard once you’ve grasped the basic concepts. Like the majority of the Quant section, probability questions only cover high school level material. The principle challenge is the tricky wording.

What Is Probability?

The first step to mastering probability is to break down the basic idea:

Probability = the number of desired outcomes / the total number of outcomes

Or in other words, the chance of something happening is the quotient of the number of desired outcomes and the total number of possible outcomes.

A coin flip is one generic example that can help us understand probability.

There are two possible outcomes when we flip a coin: heads or tails. If we want the coin to land on heads, then we divide 1 (the chance that the coin will land on the desired outcome, heads) by 2 (all possible outcomes, heads and tails), and the result is ½ or 0.5 (50%), meaning that there is a 50% chance that the coin will land on heads.

Although this is an elementary example, it demonstrates the fundamental concept behind all probability problems–a ratio between a part and a whole expressed as a fraction or percentage.

Probability of Independent Events

The probability of x discrete events occurring is the product of all individual probabilities.

For example, imagine that we toss a coin twice. Each toss is independent of the other, meaning that each toss has an equal chance of landing on either heads or tails (0.5). If we want to calculate the chance of getting heads twice in a row, we need to multiply the probability of getting heads the first time by the probability of getting heads the second time.

Or, represented as an equation:

½ x ½ = ¼

We get a 0.25 or 25% chance that the coin will land on heads twice.

Probability of Getting Either A or B

Keep in mind that the sum of all possible events is equal to 1 (100%).

If we continue with the coin toss example, we know that the probability of landing on heads is 0.5, and that the probability of landing on tails is also 0.5. Therefore:

0.5 + 0.5 = 1

The possibility of landing on either heads or tails is equal to 1, or 100%. In other words, every time we flip a coin, we can be certain that it will land on heads or tails.

Probability Of An Event Not Occurring

Following the concept that the sum of all possible events is 1, we can conclude that the probability of event A not happening (A’) is 1 – A, or equal to the probability of event B occurring.

The chance that the coin will not land on heads is equal to the chance that the coin will land on tails:

1 – 0.5 = 0.5

This method is most useful in situations with many favorable events and fewer unfavorable ones. Since time management is essential on the GMAT, it’s better to avoid solution paths that require more calculations. Subtracting the number of unfavorable events from the whole is quicker and simpler, and thus, less likely to result in mistakes.

Pay Attention to Keywords

Read each problem’s wording with great care to determine exactly which operations to use.

For example, if the problem uses the word “and,” you need to find the product of the probabilities. If the question uses the word “or,” you need to solve for their sum.

If we flipped one coin and we wanted to know the chances of landing on either heads or tails, we would calculate it like this:

0.5 + 0.5 = 1

Similarly, if we were to toss two coins and we wanted to find the probability of landing on both heads and tails, we would use this equation:

0.5 x 0.5 = 0.25

Avoid Common Errors

Minor errors, such as missing possible events, can lead to incorrect answers.

These pointers will help you avoid some common mistakes on probability questions:

• List all possible events before starting any calculations;
• Sum up the probabilities of all possible events to make sure they add up to 1;
• If there are several different arrangements possible (for example, picking different colored balls from a box), find the probability of one of the events and multiply it by the number of different possible arrangements.

If you enjoyed this article make sure to check out our other How To articles like: & Verbal section.

Posted on
17
Sep 2020

Which Is The Greatest – GMAT Problem

Today we’re going to look at a GMAT problem that screams for estimation but can really tie you in knots if you don’t have the right pivot question, the right perspective. Of the following which is greatest? And on its surface this would seem like a straightforward question except of course the GMAT being the GMAT they’re going to give you a bunch of numbers that are going to be hard to interpret. One part of this problem is simply training. The square root of 2, the square root of 3, the square root of 5. These are common, especially root 2 and root 3 because we see them a lot on triangle problems.

Get Familiar With Identities

And knowing these identities by heart as an estimate is really, really valuable just for being able to get a bearing whether you’re on a geometry problem and you’re trying to navigate or make sure that your answer seems correct or if you’re in a problem like this knowing these identities root 2 is 1.4, root 3 is 1.7, root 5 is 2.2 is useful as a touchstone.

Break Down The Problem

But this problem in general and the greater problem can be broken down not by saying oh well this is 1.4, this is 1.7, but by asking ourselves well logically which is bigger which is smaller. Remember it’s a multiple choice exam and they’re asking for the biggest or the smallest or whatever it is but these are opportunities to compare not nail down knowledge and this attitude is exceptionally vital for the data sufficiency but it crops up in problem solving a lot more than people might care to admit.

Especially if you’ve been there just trying to study and study and study and get to a precise answer on a lot of these things. So, let’s start just by taking a look at a few things. First square root of three square, root of two which one’s larger? If you said root three you are correct. How much larger? That might be a little bit more difficult to ascertain but if you say 1.7 versus 1.4 maybe 20 percent larger 3 is 50% larger than 2 so root 3 is going to be some smaller percentage larger than root two. But either way we know that root three is the bigger one it’s going to be the dominant value so the question becomes how much larger? Or which part of the answer drives the answer choice?

What Do We Know?

So we know that the integers 2 and 3 are more meaningful, larger than the square roots because the square roots are components of those integers. So between A and B, a drives the question that is the three drives the root two more than the two drives the root three. We can take a look at the following two and notice that both of them are around root three.

That is if we take apart the ugly part, which is the square root and take a look at the rest of it – four over five, five over four, these numbers are about one and compared to the two root three we have and the three root two which we’ve already decided is even stronger we don’t really need to entertain C and D all that much. Just to understand that oh they’re about a root three and that’s not going to be enough.

Finally, we have E. E is a little funky but we can ask ourselves how many times will root 3, will this 1.7 go into 7 and we get this answer that it’s a bit below 4. Compared with 3 root 2 which is 4.2 (3 times 1.4), we still have a driving the answer. You guys see how this is a marriage of doing a little bit of estimation but also really keeping your framing as is this greater or less than. Now we’ve included a bunch of other different answer choices here for you to take a look at play around with it and see if you can get yourself familiar with comparing these things because the GMAT is only going to come at you with things like square roots that are unfamiliar.

So it’s a fairly defined GMAT problem in that sense. I hope this helps, questions below, like us, subscribe, keep checking in and we’ll see you again real soon.

If you enjoyed this GMAT problem, try these problems next: Probability problem, and the

Posted on
06
Aug 2020

Probability GMAT Problem

Probability GMAT Problems can be super complex if you don’t frame it correctly. One of the keys to looking at probability problems, particularly conditional probability and independent probability problems, is breaking each part up into its own entity, and a lot of times this clarifies the problem.

Introduction To The XYZ Probability Problem

Let’s take a look at this ‘XYZ’ probability problem. Xavier, Yvonne, and Zelda are solving problems. We’re given the 3 probabilities for correct answers and we’re being asked what’s the probability of X being right and solving it, Y solving it, and Z not solving it.

The first thing we can look at is, say: “Well what’s the probability of Zelda not solving it?” And it’s just going to be the flip, the other side of 5/8 to bring us up to 1. If she solves it 5 out of 8 times, she’s not going to solve it the other 3 out of 8 times. So, we’re dealing with 1/4, 1/2, and 3/8.

Doing The Math May Seem Simple

The math here is straightforward, multiply them together. But that might not be readily apparent, or at the very least, just plugging it into that formula can get you into trouble. So, here’s where owning it conceptually and mapping it out with a visualization helps you take command of this problem.

Xavier Getting It Correct

Since each probability is independent of the others we can look at them independently. What’s the probability of Xavier getting this correct? 1 out of 4 times. So, we can say in general, for every four attempts, he gets it correct once or 25%. If, and only if Xavier gets it correct can we move on to the next part – Yvonne.

Yvonne Getting It Correct

Xavier gets a correct 1 out 4 times then what are the chances that Yvonne gets a correct? 1 out of 2. So to have Xavier get it correct and then Yvonne get it correct it’s going to be 1 out of 8 times – 1/4 times 1/2.

It’s not that we can’t look at a Yvonne when Xavier gets it incorrect, it’s that it doesn’t matter. From a framing perspective, this is all about only looking at the probability for the outcome that we want and ignoring the rest.

Zelda Getting It Incorrect

Xavier: 1 out of 4, Yvonne: 1 out of 2, gets us to 1 out of 8. Then and only then, what are the chances that Zelda gets it incorrect? 1 out of 8 trials brings us to X and Y are correct, then we multiply it by the 3/8 that Zelda gets it incorrect. That gets us to 3/64. 3 out of every 64 attempts will end in ‘correct’, ‘correct’, ‘incorrect’.

This is one of those problems that may have to go through a few times but once you attach the explanation to it, you can’t mess up the math.

If you enjoyed this GMAT probability problem, try your hand at these other types of challenging problems: &

Posted on
09
Jul 2020

8 GMAT Test Strategies To Help Boost Your Score

By: Apex GMAT
Contributor: Ivan Minchev
Date: 9th July, 2020

More than 250,000 students take the GMAT every year as a requirement to get into the thousands of different MBA, EMBA, MFin, MAcct and Management PhD programs worldwide. However, due to the complexity of the exam as well as its adaptive difficulty only the top 12% of test-takers manage to score 700 or above. Here are 8 GMAT test strategies you can utilize to achieve a higher score on the exam, no matter where you currently are on your GMAT preparation journey.

Perspective  is everything. It is very important to understand that even though getting in the top 10% of test-takers might seem like a spectacular achievement (and don’t get me wrong, it certainly is) setting your goals on a certain score tends to be counterproductive. Instead, focus on attaining specific skills, knowledge, and command, and the score will follow. Goals lead to expectations and fear of failure, and fear of failure in turn results in stress, which can greatly hinder performance.

2. Overcoming stress!

Stress and fear can greatly influence your results, but there are ways to manage these very normal responses to a high stakes situation. One of the ways to reduce stress and boost your confidence is by beginning your preparation process as early as possible – ideally 90-120 days before the exam. This provides enough time to fully grasp the complexities of the exam, and more importantly internalize a new set of skills to handle that complexity.

A test taker’s greatest enemy is test anxiety. Understand that anxiety happens to everyone. What sets top performers apart is how they handle that anxiety, and how they direct it back into their performance. Many people use a variety of relaxation techniques for dealing with test anxiety. The most common and easy to use method is to practice deep and controlled breathing in combination with visualization techniques.

3. For exam day…

Are you a coffee drinker? Surprisingly, caffeine can really help your performance on test day. Caffeine is a powerful nootropic that will help keep your senses sharp and will also boost the oxygenated blood flow to your brain, subsequently enhancing your performance. For more info on how coffee affects your performance

Remember how we said that it’s important to begin your exam prep early? This “early bird” attitude can be applied in more ways than one. What this implies is that you must (not might, not should) prepare your GMAT Test Day Survival Kit on the previous day and not leave this for the last moment. Everyone has waited for the last minute to do something, and chances are everyone has left something crucial behind. With the GMAT being such an important exam such situations should be avoided as much as possible. Try having a mock exam day. Map out the whole test day and practice it as if it were real, including your trip to the testing center. This will help you normalize the process and alleviate anxiety on test day.

4. Value your time and manage it efficiently!

Since the GMAT is a timed exam one’s planning and strategic skills are put to the test as they have to come up with an efficient time management strategy.

Use mental math tools whenever possible and also try getting used to reading and analyzing charts, graphs and tables efficiently for the Integrated Reasoning section.

Once you’re further along in your preparation and have mastered seeing multiple solution paths before engaging any of them, familiarize yourself with common problems, and built up test reading and perspective skills, then you can begin dedicating yourself to timed sets: working on a cluster of 10 consecutive questions for each section of the exam when on the clock. This helps you calibrate your timing decisions and more readily notice when they require adjustment.

Remember, just because the GMAT is a timed exam, this doesn’t mean we must learn under a time constraint. Like good cooking, good learning takes time. Give yourself sufficient time to learn, while also making sure the learning time is spent as productively as possible.

5. The Integrated Reasoning section

Dealing with 12 multi-part questions in 30 minutes means that you’re going to be overwhelmed with information, and you won’t have much time to spare. Sorting through large amounts of data and understanding it in a timely manner is key to getting through this section.

A good way to rapidly identify information needed to solve a problem is knowing what to look for. Read the problems carefully (and this applies to all sections) and proactively determine what you want out of the information or solution path. This way, you will sift out most unnecessary information in advance, saving plenty of time along the way. However, this does NOT mean to ignore the text written around the tables/graphs/charts.

6. The Analytical Writing section

Failing to plan is planning to fail! Always plan your essay! Set aside 4-5 minutes to plan what you are going to write and how you are going to structure your essay.

Create an essay template in advance! There are many ways you can go about making one but usually, the more you practice your essay writing skills the more used to a specific writing style you are going to get ultimately resulting in your own template.

There is nothing embarrassing about asking for help, especially when it comes to an exam that is so vital to one’s future. There are numerous GMAT forums and courses on the web, where you can ask and get help from people who have already taken it.

However, if you would prefer a more personal and individualized approach you could consider hiring a private tutor. The benefit of not preparing alone but hiring a tutor is that it allows for direct feedback on what are an individual’s strengths and what needs improvement, while also receiving advice on how to achieve those improvements. As a result, when the exam day comes you will not only be well prepared but will also know it, having built up confidence in your abilities.

8. Practice, practice, practice!

No doubt you’re familiar with the phrase “practice makes perfect.” There is a reason why this is such a popular saying: it’s true! Not all practice is equal, though. Varied practice that aims at building on existing skills and knowledge is much more high yielding than repetition. No matter how clever you are, no matter how good of a student you’ve been or how proficient in math you are if you do not put enough time and effort in your prep you are not likely to be happy with the end result. Even the top tutors and courses out there won’t be able to help you out if you don’t give your best. So remember, don’t just go through the motions, but practice by constantly looking at the same problems and concepts in new ways, and trying to use them in novel situations, and you’ll find your GMAT prep vastly accelerated.

That was the list of 8 strategies to help you score high on the GMAT. Keep in mind that what works for one person will not necessarily work for another as everybody learns differently. It is only through practice and proactive learning that you will be able to find what are the best methods for your success.

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.

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:

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