An Introduction to combination math
Posted on
23
Feb 2021

An Intro to Combination Math

By: Rich Zwelling (Apex GMAT Instructor)
Date: 23 Feb 2021

Last time, we looked at the following GMAT combinatorics practice problem, which gives itself away as a PERMUTATION problem because it’s concerned with “orderings,” and thus we care about the order in which items appear:

At a cheese tasting, a chef is to present some of his best creations to the event’s head judge. Due to the event’s very bizarre restrictions, he must present exactly three or four cheeses. He has brought his best cheddar, brie, gouda, roquefort, gruyere, and camembert. How many potential orderings of cheeses can the chef create to present to the judge?

A) 120
B) 240
C) 360
D) 480
E) 600

(Review the previous post if you’d like an explanation of the answer.)

Now, let’s see how a slight frame change switches this to a COMBINATION problem:

At a farmers market, a chef is to sell some of his best cheeses. Due to the market’s very bizarre restrictions, he can sell exactly two or three cheeses. He has brought his best cheddar, brie, gouda, roquefort, gruyere, and camembert. How many potential groupings of cheeses can he create for display to customers? 

A) 6
B) 15
C)
20
D) 35
E) 120

Did you catch why this is a COMBINATION problem instead of a PERMUTATION problem? The problem asked about “groupings.” This implies that we care only about the items involved, not the sequence in which they appear. Cheddar followed by brie followed by gouda is not considered distinct from brie followed by gouda followed by cheddar, because the same three cheeses are involved, thus producing the same grouping

So how does the math work? Well, it turns out there’s a quick combinatorics formula you can use, and it looks like this: 

combinations problem

Let’s demystify it. The left side is simply notational, with the ‘C’ standing for “combination.” The ‘n’ and the ‘k’ indicate larger and smaller groups, respectively. So if I have a group of 10 paintings, and I want to know how many groups of 4 I can create, that would mean n=10 and k=4. Notationally, that would look like this:

combinatorics and permutations on the GMAT, combination math on the gmat

Now remember, the exclamation point indicates a factorial. As a simple example, 4! = 4*3*2*1. You simply multiply every positive integer from the one given with the factorial down to one. 

So, how does this work for our problem? Let’s take a look:

At a farmers market, a chef is to sell some of his best cheeses. Due to the market’s very bizarre restrictions, he can sell exactly two or three cheeses. He has brought his best cheddar, brie, gouda, roquefort, gruyere, and camembert. How many potential groupings of cheeses can he create for display to customers? 

A) 6
B) 15
C)
20
D) 35
E) 120

The process of considering the two cases independently will remain the same. It cannot be both two and three cheeses. So let’s examine the two-cheese case first. There are six cheese to choose from, and we are choosing a subgroup of two. That means n=6 and k=2:

combinations and permutation on the gmat, combination math on the gmat

Now, let’s actually dig in and do the math:

combinatorics and permutations on the GMAT, combination math on the gmat

combinatorics and permutations on the GMAT, combination math on the gmat

From here, you’ll notice that 4*3*2*1 cancels from top and bottom, leaving you with 6*5 = 30 in the numerator and 2*1 in the denominator:

combinatorics and permutations on the GMAT, combination math on the gmat That leaves us with:

6C2 = 15 combinations of two cheeses

Now, how about the three-cheese case? Similarly, there are six cheeses to choose from, but now we are choosing a subgroup of three. That means n=6 and k=3:

solving a combinatorics problem

From here, you’ll notice that the 3*2*1 in the bottom cancels with the 6 in the top, leaving you with 5*4 = 20 in the numerator:

combination problem on the gmat answer

That leaves us with:

6C3 = 20 combinations of three cheeses

With 15 cases in the first situation and 20 in the second, the total is 35 cases, and our final answer is D. 

Next time, we’ll talk about what happens when we have permutations with repeat elements.

In the meantime, as an exercise, scroll back up and return to the 10-painting problem I presented earlier and see if you can find the answer. Bonus question: redo the problem with a subgroup of 6 paintings instead of 4 paintings. Try to anticipate: do you imagine we’ll have more combinations in this new case or fewer?

Permutations and Combinations Intro
A Continuation of Permutation Math
An Intro To Combination Math
Permutations With Repeat Elements

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Posted on
16
Feb 2021

Triangles With Other shapes

By: Rich Zwelling (Apex GMAT Instructor)
Date: 16 Feb 2021

As discussed before, now that we’ve talked about the basic triangles, we can start looking at how the GMAT can make problems difficult by embedding triangles in other figures, or vice versa. 

Here are just a few examples, which include triangles within and outside of squares, rectangles, and circles:

triangles in other shapes GMAT article

Today, we’ll talk about some crucial connections that are often made between triangles and other figures, starting with the 45-45-90 triangle, also known as the isosceles right triangle.

You’ve probably seen a rectangle split in two along one of its diagonals to produce two right triangles:

triangles in other shapes gmat article gmat probelm

But one of the oft-overlooked basic geometric truths is that when that rectangle is a square (and yes, remember a square is a type of rectangle), the diagonal splits the square into two isosceles right triangles. This makes sense when you think about it, because the diagonal bisects two 90-degree angles to give you two 45-degree angles:

triangles in other shapes gmat article, 45 45 90 degree angle

(For clarification, the diagonal of a rectangle is a bisector when the rectangle is a square, but it is not a bisector in any other case.)

Another very common combination of shapes in more difficult GMAT Geometry problems is triangles with circles. This can manifest itself in three common ways:

  1. Triangles created using the central angle of a circle

triangle in a circle, gmat geometry article

In this case, notice that two of the sides of the triangle are radii (remember, a radius is any line segment from the center of the circle to its circumference). What does that guarantee about the triangle?

Since two side are of equal length, the triangle is automatically isosceles. Remember that the two angles opposite those two sides are also of equal measure. So any triangle with the center of the circle as one vertex and points along the circumference as the other two vertices will automatically be an isosceles triangle.

2. Inscribed triangles

triangle inscribed in circle, gmat problem

An inscribed triangle is any triangle with a circle’s diameter as one of its sides and a vertex along the circumference. And a key thing to note: an inscribed triangle will ALWAYS be a right triangle. So even if you don’t see the right angle marked, you can rest assured the inscribed angle at that third vertex is 90 degrees.

3. Squares and rectangles inscribed in circles

rectangle in circle, gmat geometry

What’s important to note here is that the diagonal of the rectangle (or square) is equivalent to the diameter of the circle.

Now that we’ve seen a few common relationships between triangles and other figures, let’s take a look at an example Official Guide problem:

A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A) 19,200
B) 19,600
C) 20,000
D) 20,400
E) 20,800

Explanation

The diagonal splits the rectangular park into two similar triangles:

triangle in other shapes gmat problem

Use SIGNALS to avoid algebra

It can be tempting to then jump straight into algebra. The formulas for perimeter and diagonal are P = 2L + 2W an D2 = L2 + W2, respectively, where L and W are the length and width of the rectangle. The second formula, you’ll notice, arises out of the Pythagorean Theorem, since we now have two right triangles. We are trying to find area, which is LW, so we could set out on a cumbersome algebraic journey.

However, let’s try to use some SIGNALS the problem gives us and our knowledge of how the GMAT operates to see if we can short-circuit this problem.

We know the GMAT is fond of both clean numerical solutions and common Pythagorean triples. The large numbers of 200 for the diagonal and 560 for the perimeter don’t change that we now have a very specific rectangle (and pair of triangles). Thus, we should suspect that one of our basic Pythagorean triples (3-4-5, 5-12-13, 7-24-25) is involved.

Could it be that our diagonal of 200 is the hypotenuse of a 3-4-5 triangle multiple? If so, the 200 would correspond to the 5, and the multiplying factor would be 40. That would also mean that the legs would be 3*40 and 4*40, or 120 and 160.

Does this check out? Well, we’re already told the perimeter is 560. Adding 160 and 120 gives us 280, which is one length and one width, or half the perimeter of the rectangle. We can then just double the 280 to get 560 and confirm that we do indeed have the correct numbers. The length and width of the park must be 120 and 160. No algebra necessary.

Now, to get the area, we just multiply 120 by 160 to get 19,200 and the final answer of A.

Check out the following links for our other articles on triangles and their properties:

A Short Meditation on Triangles
The 30-60-90 Right Triangle
The 45-45-90 Right Triangle
The Area of an Equilateral Triangle
Isosceles Triangles and Data Sufficiency
Similar Triangles
3-4-5 Right Triangle
5-12-13 and 7-24-25 Right Triangles

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Combinatorics: Permutations and Combinations Intro
Posted on
11
Feb 2021

Combinatorics: Permutations and Combinations Intro

By: Rich Zwelling (Apex GMAT Instructor)
Date: 11 Feb 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. 

Permutations and Combinations Intro
A Continuation of Permutation Math
An Intro To Combination Math
Permutations With Repeat Elements

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Isosceles Triangles and Data Sufficiency title
Posted on
26
Jan 2021

Isosceles Triangles and Data Sufficiency

By: Rich Zwelling (Apex GMAT Instructor)
Date: Jan 21, 2021

Although we’ve already discussed isosceles triangles a bit during our discussion of 45-45-90 (i.e. isosceles right) triangles, it’s worth discussing some other contexts in which you may see isosceles triangles on the GMAT, specifically on Data Sufficiency problems. 

As we discussed before, an isosceles triangle is any triangle that features two equal sides and thus two equal opposite angles:

Isosceles Triangles and Data Sufficiency picture 1

That’s an easy enough definition to remember, but how does the GMAT turn this into more challenging problems? For that, let’s take a look at the following Official Guide problem. Try to solve before reading the explanation below the problem:

Isosceles Triangles and Data Sufficiency picture 2

In the figure above, what is the value of x + y ?
(1) x = 70
(2) ABC and ADC are both isosceles triangles

Explanation

In this case, it’s straightforward enough to determine that each statement alone will be insufficient. Statement (1) gives us a definitive value for x, but no information about y, thus we cannot answer the question (the value of x+y). And although Statement (2) labels each triangle in the diagram as isosceles, we have no way of knowing the specific angles involved nor their relationships. 

However, as with many Data Sufficiency problems, especially those involving Geometry, things can get thorny when we have to combine the statements. The two statements look very complimentary, and that could lead us to prematurely conclude the answer is C (i.e. the two statements are sufficient when combined). But we must do a thorough check. 

Reframing the question

Remember that at any point during a Data Sufficiency problem — beginning, middle, or end — you can reframe the question for simplicity. The question asks for the value of x+y. But now that we are combining the statements, we already know that x=70. In terms of sufficiency, then, what information do we need? The only thing missing is a definitive value of y. The question now might as well be “What is the value of y?”

Now, here’s where the GMAT thinking really comes into play. It’s one thing to understand what an isosceles triangle is. It’s quite another to judge what a diagram of an isosceles triangle does or does not tell you and what you can or cannot extrapolate from it. 

One of my personal favorite things about Geometry Data Sufficiency problems is that they tend to be very intuitive visually. You can often answer them by manipulating figures. 

We know that triangle ADC is isosceles, but is that enough to give us definitive measurements? Visually, which of these does it look like?  

Isosceles Triangles and Data Sufficiency picture 3

Without any numerical evaluations, we can see that we can’t get a definitive measure for the angle at D, which in this case is our y. So even when we combine the statements, we cannot get an answer to our question. The correct answer is E

Here’s another case of a tricky Data Sufficiency problem involving isosceles triangles:

In isosceles triangle RST, what is the measure of angle R?

  • The measure of angle T is 100 degrees
  • The measure of angle S is 40 degrees

Again, give the problem a shot before reading the answer and explanation.

Explanation

This is one for which you can draw a diagram, but it’s not necessary. The trick here is to remember another key property of triangles, namely that all angles in the triangle must sum to 180 degrees.

Since the triangle is isosceles, and since each statement gives you only one angle of three, the temptation can be to say that each statement is insufficient on its own. This is certainly the case for Statement (2), because the 40-degree angle could be one of a pair (in which case we would have a 40-40-100 triangle) or the 40-degree angle could be the odd angle out (in which case we would have a 40-70-70 triangle). 

Because the problem asks for the value of R, and since R could be 40, 70, or 100 depending on the situations outlined above, Statement (2) is INSUFFICIENT.

However, there’s a catch when evaluating Statement (1). Notice that angle T is an obtuse angle, meaning it is greater than 90 degrees. Is it possible that there are two 100-degree angles in a triangle? This would produce a total of 200 degrees, which would exceed the 180-degree total for any triangle. As such, the only possibility is that the 100 degree angle is the odd angle out, and the other two angles are equal acute angles (specifically, we have a 40-40-100 triangle). 

Now we know R must be 40 degrees. Statement (1) is sufficient, and the correct answer is A.

But notice how the GMAT sets the statements up to bait you into thinking that you must combine the two statements to figure out the value of angle R. 

Now that we’ve finished talking about the basic triangle types, we can move on to talking about what happens when triangles are used within different shapes. In the meantime, here are links to our other triangle articles:

A Short Meditation on Triangles
The 30-60-90 Right Triangle
The 45-45-90 Right Triangle
The Area of an Equilateral Triangle
Triangles with Other Shapes
Isosceles Triangles and Data Sufficiency
Similar Triangles
3-4-5 Right Triangle
5-12-13 and 7-24-25 Right Triangles

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Featured Video Play Icon
Posted on
21
Jan 2021

Rope Problem – Graphic Solution Path

Hi guys! Today we’re going to look at the rope problem. And this is a fairly straight forward problem with an excellent graphic solution path. But there are some obstacles in our way to that graphic solution path.

Obstacles To Avoid

The first thing to watch out for here is the phrasing of the problem. You’ll notice it is phrased in an awkward way: rather than telling us where the rope is cut, it tells us one length relative to the other. The other obstacle is that we immediately want to jump into the math. Either setting up an algebraic equation or, otherwise, not visualizing the rope.

And this is an error not because it’s that much more difficult to do it mathematically, but because it’ll take you a bit more time and it will be less clear. You won’t be as confident in your answer choice relative to actually being able to see it.

Visualize the Problem

So, what you want to do is visualize the actual rope. And we’ve got one right here. So, if this is 40 feet long, and one side is 18 feet longer than the other then we wanna take the 18 and make that the longer piece, and then the other two pieces are distributed among the short side and the rest of the long side. Once we have that we can say, well, if this long part here is 18, then these two pieces must be 22 they also must be equal. And this is much quicker and clearer than setting up an equation 2x+18 = 40

We’re doing the same thing but here it’s easy to say: okay, 11; 11+18 is 29, that gets us our 40. And we’re there, we’re confident, we move on.

This is a great example of a straightforward problem that can be done in 15 seconds and if you’re doing it in a minute you’re spending too much time. Hope this helps, and we’ll see you guys next time!

For other problem related to this, try out the Test Averages Problem.

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Featured Video Play Icon
Posted on
14
Jan 2021

Averages Problem No.1 : Test Averages

Hey guys, today we’re going to take a look at the test averages problem. This is a very straightforward mathematically oriented average problem or at least it can be. But there are very strong graphic solution paths here and there’s also a really strong sort of intuitive running tally counting solution path here. We’re going to start out with the math though, just because that’s how a lot of people are familiar with this problem. Before we jump into the heavier duty quicker sort of stuff. 

Doing the Math

So to solve this problem we want to take an average. But one of the components of our average is missing. So we have four things with an average of 78, and a fifth unknown. That means we can assume that each of the first four exams were 78. So we’ve got 4 times 78 plus X over 5. The total number of exams is going to give us our average of 80. Then through algebra, algebraic manipulation we multiply the 5 over, we get 400 equals 4 times 78 plus x. The 4 times 78 is 312. We subtract that off the 4 and that brings you to 88. Answer choice E.

Graphic Solution Path: Poker Chips

Let’s take a look at this a little differently. One of the ways I like looking at averages is imagining stacks of poker chips and you can have stacks of anything. I like poker chips because they fit together and you can make two stacks equal very easily so what we’re being told here is we have four stacks of 78 a fifth unknown stack but if we equalize them all that is if we take chips off of the unknown stack and distribute them all the stacks will be 80. That means that the fifth stack needs to be 80 and then it needs two poker chips for each of the other four stacks to bring those 78’s up. We can also envision this as just a rectangle our goal is 80 but we have 78, and our goal is five tests but we have four so we have 78 by four here. And then 80 by 5 here what’s missing is the full 80 and then 2 on each of four stacks of 48.

Running Tally Method: Intuitive Approach

The most powerful way to handle this problem though is probably by doing a running tally. Don’t even worry about the visualization but rather notice that, I’ve got 47 8s each of those are too short so I’m two, four, six. eight points short on the last test. I need to get the 80 that I want plus those eight points that I’m short bringing us to 88. And anybody who’s sweated like A+, B+, A- or a C+, B- has done this math. So if you characterize it like that a lot of times it becomes much more intuitive and once again allows you to cultivate confidence for a deeper treatment and more complex averages problems and mean problems check out the snack shop problem, check out the company production problem and there’s a great ds problem that we do the trade show problem you’ll find links to all of them just below and I hope this helped. 

 

Enjoyed this Averages Problem ? Try another type of GMAT problem to get familiar with all question types on the exam: Remainder Number Theory Problem.

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45-45-90 triangles on the gmat
Posted on
06
Jan 2021

45-45-90 Right Triangle – GMAT Geometry Guide

By: Rich Zwelling (Apex GMAT Instructor)
Date: Jan 6 2021

45-45-90 Right Triangle

Another of the commonly tested triangles on the GMAT is the 45-45-90, also known as the isosceles right triangle. Know that term, as it could appear by name in a question.

As shown in the above diagram, the side lengths of this triangle always fit the same ratio (1 : 1 : √2) , where the legs are the same length and the hypotenuse length is √2 times the leg length. For example, if the leg lengths were 3 instead of 1, then the hypotenuse would be 3√2 instead of simply √2.

But likewise, don’t forget that you can go backwards and divide the hypotenuse length by √2 to get to the leg length. It may seem obvious, but it presents an important point: what’s more important than simply memorizing the ratio is understanding the mathematical relationship between the side lengths. This will help you avoid trouble if the GMAT happens to give you a problem that doesn’t conform to expectations.

For example, the following problem fits expectations quite nicely:

A yard in the shape of an isosceles right triangle has a hypotenuse of length 10√2. What is the area of this yard?

From this information, it’s easy enough to deduce that the leg length is 10, and we can draw a diagram that looks roughly like this:


From there, we can easily calculate the area, which is base*height / 2, or in this case 10*10/2 = 50.

But what happens if we give the problem a little twist:

A yard in the shape of an isosceles right triangle has a hypotenuse of length 10. What is the area of this yard?

Did you catch the twist? We’re used to the hypotenuse including a √2. This is what the GMAT will do. They’ll throw you off-center, and you’ll have to adjust. But this is also why we said earlier that what matters more than memorizing the ratio of sides is understanding the relationships between the sides of an isosceles right triangle…

Remember we said that, just as we multiply the leg length by √2 to get to the hypotenuse length, so we must divide the hypotenuse length by √2 to get to the leg length. That must mean each leg has length 10/√2. 

You can then take 10/√2 and multiply it by √2/√2 to de-radicalize the denominator and get (10√2) / 2, or a leg length of 5√2:

Notice again that we have a more unfamiliar form, with the √2 terms in the legs and an integer in the hypotenuse. We can’t count on the GMAT to give us what we’re used to. 

Now we can calculate the area:

Area = (base*height)/2 = (5√2)(5√2)/2 = (5*5)(√2*√2)/2 = (25)*(2) / 2 = 25

 

Problem #1

Now, to try this on your own, take a look at this Official Guide problem:

If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

(A)   40
(B)   60
(C)   80
(D)   100
(E)   120

Explanation:

This is a nice change-up, because it involves another shape. Did you notice that splitting a square along its diagonal creates two isosceles right triangles

Once you realize this, you can divide 20 by √2 to get 20/√2, then multiply top and bottom by √2 to get x=10√2.

Since the question asks for perimeter, we can multiply this by four to get 40√2. 

The final step is to realize that √2 is approximately 1.4. If we multiply 40 by 1.4, the only answer choice that possibly makes sense is 60, and thus the correct answer is B

 

After reviewing the 45-45-90 triangle identity, these further articles in the triangle geometry series will take you through more identities, each of the specific triangles and how the GMAT uses them to test your critical and creative solving skills:
A Short Meditation on Triangles
The 30-60-90 Right Triangle
The 45-45-90 Right Triangle
The Area of an Equilateral Triangle
Triangles with Other Shapes
Isosceles Triangles and Data Sufficiency
Similar Triangles
3-4-5 Right Triangle
5-12-13 and 7-24-25 Right Triangles

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MBA Admissions consulting
Posted on
05
Nov 2020

MBA Admissions Consulting: Which Exam is Right For You

by ApexGMAT

Contributors: Fatma Xhafa & Svetozara Saykova

November 5, 2020

 

Are you ready to get a Master’s degree and take the business world by a storm? The first thing to consider is which admissions exam to prepare for. There are a handful of tests that MBA programs use to assess applicants. The GMAT, GRE, EA, INSEAD, and  ieGAT are the most common. Generally, these exams are more alike than not, but each exam presents unique challenges. APEX consultants can help you decide which is right for you.

 

Table of contents

  • The GMAT
  • The GRE
  • The Executive Assessment
  • The INSEAD Assessment
  • The ieGAT Assessment

GMAT

The Graduate Management Admissions Test, commonly known as the GMAT, is an assessment administered by the Graduate Management Admissions Council (GMAC). It is used for admission to MBA programs around the globe. 

The GMAT consists of 4 sections—Integrated Reasoning, Analytical Writing Assessment, Verbal, and Quantitative. Each section examines a particular set of essential business skills. The GMAT tests a variety of skills due to its computer adaptive nature, which is also what makes it so challenging.  

 

GMAT Sections Types of Questions Duration
Analytical Writing Assessment
  • short essay
30 minutes
Integrated Reasoning
  • multi-source reasoning
  • table analysis
  • graphics interpretation
  • two-part analysis
30 minutes
Verbal
  • sentence correction
  • reading comprehension
  • critical reasoning
65 minutes 
Quantitative
  • problem solving
  • data sufficiency 
61 minutes

 

The total price for sitting the GMAT is $250 (as of October 2020 €230 , £203). This includes sending the official scores to five MBA programs of your choice. Due to the COVID-19 pandemic, the GMAT is also offered online until December 2020. 

A 700+ GMAT score can open doors to some of the world’s most elite MBA programs, so don’t hesitate! Apex’s dedicated tutors can help get you there; time zone differences, busy schedules, and distance are nonissues for our team. Schedule a call at your convenience to discuss prep options and jumpstart your journey to success. 

GRE 

The Graduate Record Examination, or the GRE for short, is facilitated by the Educational Testing Service (ETS). Thousands of MBA, MS/MA and Ph.D programs accept the GRE.

There are two types of GRE—the General Exam and the Subject Test. The General Exam is designed to examine analytical writing, quantitative ability, and verbal reasoning skills, and the Subject Test evaluates the candidate’s knowledge in a particular field of study. The subject exams include Mathematics, English Literature, Chemistry, Biology, Biochemistry, Physics and Psychology. The Subject Test is required for most specialized Master’s programs.

The General Exam consists of three sections: Analytical Writing, Verbal Reasoning and Quantitative Reasoning. The GRE has a pattern in terms of section order: the Analytical Writing section will always be the first, and can either be followed by the Verbal, Quantitative, or unscored sections in any order. 

You may be wondering what those unscored sections test for. Unscored sections only appear on the computer-based exam and vary in content. There is no set number or time allocation for unscored sections. 

Each other section, however, has a set number of problems and time limit.

GRE Sections  Computer-based GRE Paper-based GRE
Analytical Writing 1 section – 2 tasks

60 minutes

2 section – 2 tasks

60 minutes

Verbal Section  2 sections – 40 questions

60 minutes

2 section – 50 questions

70 minutes

Quantitative Section  2 sections – 40 questions 

70 minutes

2 section – 50 questions

80 minutes

Unscored varies N/A
Research  varies N/A

 

The fee for the GRE General test varies by country between $205-$255 (as of October 2020 €175-218, £159-197). The GRE Subject Test costs $150 (as of October 2020 €128, £116)

Apex’s team of experienced consultants provides personalized GRE preparation, following the most comprehensive and intensive curriculum available. Schedule a consultation to discuss your prep needs with one of our mentors. 

Executive Assessment

The Executive Assessment is designed to evaluate business school readiness based on a candidate’s experience. Many MBA programs accept this exam as an alternative to the GMAT. It’s also offered by the Graduate Management Admissions Council. 

Whereas the GMAT is a Computer Adaptive Test (CAT), the EA is a ‘multi-stage’ computer adaptive. This means that question sets are selected depending on answers to previous question sets.

The EA is designed for Executive MBA programs. As such, it’s designed for busy professionals and executives who might not have a lot of time to prepare. There are several advantages to taking the EA if you fit into this category. 

The exam consists of 3 sections: Integrated Reasoning, Verbal, and Quantitative. Each section has a 30-minute time limit, so the entire EA exam takes no more than 1.5 hours. Scores range from 100-200. All sections are weighted equally, which makes it easier to determine the total.

 

EA Sections  Questions Types of Questions
Integrated Reasoning 12
  • Multi-Source Reasoning
  • Graphics Interpretation
  • Two-Part Analysis
  • Table Analysis
Verbal  14
  • Reading Comprehension
  • Critical Reasoning
  • Sentence Correction
Quantitative  14
  • Data Sufficiency
  • Problem Solving

In addition to being only 90 minutes long, the EA is widely available in test centers. It’s possible to reschedule free of charge up to 48 hours before the appointment, and the results are available within 24 hours. Registration costs $350 (as of October 2020 €298, £268). Candidates can take the exam no more than twice.

For business programs that accept the EA, visit our featured list of EMBA programs.

Since the Executive Assessment is designed to be less time consuming than the GMAT, preparing for it also is less time consuming. Apex provides the most comprehensive EA prep on the market. Candidates can earn top scores through private tutoring, or in our EA class, which offers 10 hours of EA prep over the course of one weekend and 2 additional hours of one-on-one instruction. Find out more by scheduling a complimentary call with one of our instructors. 

INSEAD Assessment

INSEAD (Institut Européen d’Administration des Affaires) is an Executive MBA program. This program exclusively uses the INSEAD Assessment to evaluate candidates. 

The INSEAD’s structure is slightly different from the GMAT’s and as a result, the preparation is, too. It does not require an excessive amount of preparation time for math, geometry, or verbal questions. However, candidates must prepare for the exam’s format, in addition to refreshing verbal and quantitative skills.

INSEAD Sections  Number of Questions/ Time per section
Data Analysis 15 questions

30 minutes

Data Interpretation 15 questions

30 minutes

Communication Analysis 15 questions

30 minutes

Critical Thinking 15 questions

30 minutes

Case Presentation 30 minutes preparation,

15 minutes presentation

 

The exam can be taken once a month at any INSEAD campus in France, Singapore, or Abu Dhabi. Application must be submitted at least 2 weeks in advance of the exam date. Once applicants pass the pre-screening stage, they can confirm the test location and payment method. The exam costs 185 (as of October of 2020 $218, £167).

At Apex, we offer expert tutoring for the INSEAD Assessment. Our experienced instructors have extensive knowledge in everything from data analysis and interpretation to communication, critical thinking and case studies. We offer clients the flexibility to learn the ins and outs of the INSEAD in a relaxed environment.

ieGAT – IE Global Admissions Test

The ieGAT  is exclusive to the IE International University, which includes the IE business school in Spain. The ieGAT differs from the exams above in a number of ways. For starters, applicants can only take it once, so it’s highly important to be well prepared–you won’t get another shot.

In order to sit for the ieGAT, at least 25% of a candidate’s MBA application must be completed. The exam takes 80 minutes and includes 60 questions. Questions are tailored to the program that the applicant is interested in. The ieGAT is a pass/fail exam, and it’s the only test necessary for admission to IE University. 

The IE administers the Global Admissions Test in English and Spanish. The test’s language must match the language in which an applicant’s MBA program will be taught. 

ieGAT Sections 
Numerical and Verbal Reasoning
Logical – Abstract Reasoning

 

At Apex, we offer one-on-one ieGAT instruction. We provide our clients with personalized attention, flexibility, and an overall productive and enjoyable experience to ensure results. Our experts guide candidates through a multitude of solution paths in the Numerical and Verbal section, as well as the Abstract Reasoning section.

Determining which exam will help you achieve your goals might not be as simple as it seems, but talking to an experienced MBA consultant will get you started on the right path. Schedule a call with one of our consultants to discuss your aspirations, needs, and preparation options. 

Admissions Consulting 

Apex GMAT offers one-on-one tutoring for each of the exams described above. Next, it’s important to start thinking about applying to MBA programs. If you’re taking an exclusive exam, such as the ieGAT or INSEAD, you already know where you’ll be applying. Otherwise, Apex’s elite team can help you develop the skills you’ll need to land a spot in your dream program. Take the first step towards your future by scheduling a call with one of our top MBA admissions consulting experts today. 

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7 ways to improve your gmat quant score
Posted on
03
Nov 2020

7 Tips To Improve Your GMAT Quant Score

If you’ve experienced the GMAT, you may have noticed that your score is higher on some sections than others. Some otherwise strong business school candidates struggle with their score on the quantitative section. The problem might derive from preparation style, in which case, you might consider professional GMAT tutoring, a service offered by a number of organizations including Apex GMAT. Until then, these tips will help kick start your prep process so you’re ready to ace the quant section.

What’s on the GMAT Quantitative section?

First, let’s talk about what exactly the GMAT quant section consists of. Test takers have 62 minutes to answer 31 math problems. This means that on average, each question should take two minutes. However, this isn’t a hard rule, so there’s no need to get nervous if one problem takes longer than others. 

The questions are divided into two types: data sufficiency and problem-solving.

Data sufficiency questions ask test takers to analyze two given statements and determine whether the provided data tells readers enough to solve the problem. These questions are designed to evaluate quantitative fluency and critical thinking skills.

Problem-solving questions are multiple choice. They evaluate logical and analytical ability. 

Keep in mind that both question types require only algebra, arithmetic, and geometry, so there’s no need to worry about trigonometry or calculus. Moreover, all of the problems can be solved using basic high school level math. 

Why is the GMAT Quantitative section so difficult?

Based on the above description, you might think that the quant section won’t be too difficult. That isn’t exactly true. The GMAT is designed to confuse and restrict test takers in various ways. For example, each problem has a time limit and calculators aren’t allowed. Furthermore, problem solving and data sufficiency problems are in the same section, so test-takers must alternate between the two question types. These factors can cause stress. 

The following tips will help you remain calm and collected as you prepare for the quant section.

1: Don’t overthink the math

First and foremost, don’t forget that the GMAT quant section consists of simple math problems. Use this to your advantage. Don’t do all of the calculations; rather, determine what makes a problem look more difficult than it actually is. 

2: Start managing your time before the test

You can start saving time before you even pick up your pencil by practicing arithmetic. Limiting the time it takes to do simple equations means you can spend more time on the problems. Be sure to review exponent rules and brush up on decimals with fractions. And don’t forget about higher powers!

3: Use alternative strategies to find solutions

If you can’t solve a problem with simple math, try using an alternative path to the solution. There’s usually an easier way to solve quant problems–the GMAT is designed to test for efficient problem solving. Sometimes, straightforward logic or plugging in numbers will solve a problem faster. Keep in mind that a traditional approach might not be necessary for every problem. 

4: Analyze each sentence step by step

During the GMAT preparation process, learn how to simplify each question. Some problems might seem daunting, but they can be broken into smaller steps that you can solve one-by-one. Trying to solve the whole problem at once can lead test takers to answer the wrong question. The more you break down the problem, the easier it will become. Don’t worry–you’ll actually save time by (re-)reading the questions. 

Tip 5: Simplify the answer choices

In addition to simplifying the questions, the answer choices can also be simplified. For example, all data sufficiency questions use the same five answer choices: 

  1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
  2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
  3. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
  4. Each statement alone is sufficient to answer the question.
  5. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Seems wordy, doesn’t it? Fortunately, you can memorize these simpler versions:

  1. only statement 1
  2. only statement 2
  3. both statements together
  4. either statement
  5. neither statement

Tip 6: Scratch paper is a must

Although scratch paper may seem unnecessary for quant problems, it can help you keep track of calculations and clarify your thought process. It might take a little extra time, but ultimately, avoidable mistakes are even more time consuming.

Tip 7: Plug in the answer choices 

Another way to save time with alternative solution paths is to start by reading all of the answer choices and plugging them into the problem. If you don’t know which answer choices to start with, start from the middle.

Bonus tip

The most important tip of all is practice, practice, and practice! There are many different ways to prepare: memorizing rules and formulas, watching GMAT problem-solving videos (don’t forget to check out our YouTube channel), and enrolling in professional GMAT courses

Follow us to learn more about the GMAT preparation process. Good luck on your exam!

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the online gmat
Posted on
13
Oct 2020

The Online GMAT Experience-from preparation to post MBA 

by Apex GMAT

Contributor: Ilia Dobrev

 

Advancements in technology, combined with constraints caused by the COVID-19 pandemic, have prompted the GMAT world to adapt by shifting a large portion of the exam and preparation materials online. Both test takers and tutoring firms have seen positive outcomes from interactive learning aids, an abundance of resources, and easily accessible networks of people at different stages of the GMAT journey. However, the transition has also introduced some hazards concerning physical test endurance, focus, and anxiety. This article evaluates risks and challenges you may encounter taking the online exam and summarizes everything you need to know to be ready for your online GMAT experience.

The Online GMAT Exam

Since the onset of the pandemic in the spring of 2020, the General Management Admissions Council (GMAC) has introduced an innovative, completely online version of the physical GMAT test. This allows test takers to maintain social distance by sitting for the exam from the comfort of home.

As of late July, 2020, at the time of writing, anyone can schedule an online exam before December 31, 2020. In order to accommodate candidates’ availability, appointments are available 24 hours a day, 7 days a week, 24 hours before an available time slot. Note that the online GMAT exam is not available in Mainland China, Cuba, Iran, North Korea, and Sudan due to local data privacy regulations.

Differences from the regular GMAT exam

  • The GMAC has determined that the Quantitative, Verbal, and Integrated Reasoning sections are the most relevant for graduate business education. Therefore, the Analytical Writing Assessment (AWA) has been excluded from the online GMAT test.
  • The duration of the online test is shorter–2 hours and 45 minutes compared to 3 hours and 23 minutes. This time frame includes a 15 to 30 minutes tutorial to  familiarize candidates with the online proctored platform and all its functions.
  • Online, you will not be able to choose the order of the sections. The sequence is fixed as follows: Quantitative, Verbal, and Integrated Reasoning.
  • You can use a physical whiteboard, the built-in online whiteboard, or both for note taking. 

If you’re planning to use a physical white board, there are several requirements it must fulfil: it should be no larger than 12×20 inches (30×50 centimeters), use up to 2 dry erase markers and 1 dry erase whiteboard eraser. Items such as whiteboards with grids, background colors, or other markings, paper, pen, pencil, permanent marker, tissues (paper towels, napkins), whiteboard spray, chalkboards, writing tablets, and others are not permitted.

During the online exam, test takers will be able to access an online board from the icon. It contains an endless canvas to take notes on, which eliminates the need to erase your work as you progress through the sections.

  • In contrast to the two optional breaks in the regular exam, the online GMAT allows candidates to opt for only one 5-minute break before the Integrated Reasoning section.
  • Official GMAT scores are available on mba.com within 7 business days of completing the exam.
  • Another perk of the online GMAT experience is that it allows applicants to send scores to an unlimited number of institutions free of charge.
  • The online GMAT fee is $200, compared to the original $250 cost for the physical exam.
  • The online test cannot be retaken for any reason except a verified technical issue or authorized retakes.

Similarities with the regular GMAT exam

  • The online GMAT consists of the same Quantitative, Verbal, and Integrated Reasoning sections. Despite excluding the Analytical Writing Assessment (AWA), each of the other three sections contains the same number of questions as before–31, 36, and 12 respectively. In terms of timing, there are no alterations–the sections take 62, 65, and 30 minutes.

online GMAT breakdown

  • To ensure that GMAT scores are compatible and comparable across the online and test center-based versions, the online version adopts the same scoring algorithm. This means that both exams are equally replaceable with one another. 
  • Validity remains the same – 5 years.

Online GMAT Preparation, Tips & Tricks

As the online exam practically covers the same content, regular GMAT preparation remains relevant. If you are trying to figure out which prep method (self, group, or one-on-one) suits you best, you can check out the Four Ps of the best GMAT Prep. Apex’s GMAT tutors and custom-made curriculum are tailored to meet the needs for an online learning environment by providing private GMAT tutoring and nurturing constant feedback.

From a technical viewpoint, it is important to get used to the online whiteboard tool. It is available in all of GMAC’s Official Practice Exams, where anyone can practice all its functions in a simulated, timed environment. Keep in mind that you are not permitted to use touchscreens, graphics tablets, or stylus pens. And lastly, before starting the online GMAT exam, you can do a system test before to ensure your computer meets the operational requirements.

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