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Posted on
11
Aug 2021

GMAT Markup Problem – GMAT Data Sufficiency

Hey guys, today we’re going to take a look at a typically characteristic data sufficiency problem that gives us a relationship, and then asks us if we have enough to compute the final value of that relationship. There’s an algebraic solution path here, where they give us the equation and we need to see if we have all but one of the variables, that final variable being the one that they’re asking for. We can also do this via parts, scenario, and graphically, and we’ll take a look at all those as well.

GMAT Markup Problem Introduction

GMAT Markup Problem

This problem describes to us the relationship between the selling price, the cost, and the markup. And notice that, while we’re going to sketch it out here, the actual relationship doesn’t matter to us – all that matters is that if they’re asking for one term in terms of the rest if we have the other terms, that’ll be enough.

Algebraically we have selling price S equals the cost C plus the markup M. So this is giving us the markup in, let’s say dollar terms, whereas we might also set this up as selling price equals cost times one plus the markup percentage. And here we just have that notational shift. So, what we’re looking for, if we want to know the markup relative to the selling price, is an understanding of it either relative to the selling price or relative to the cost. That is, these two things are associated and the markup, when associated with the cost, gives us a ratio. Where the markup, when associated with the selling price, is a fraction. And if you’ll remember notationally these things are expressed differently, but conceptually there’s the same math behind it.

Statement 1

Number one gives us in percentage terms the mark up compared to the cost. So, here we can see it as 25% more and this is where it ties into that second version of the algebraic one we just looked at. The cost we can break up into four parts of 25% so that when we add the markup that’s a fifth part. Therefore, the markup comprises one-fifth or 20% of the selling price.

Statement 2

Number two provides us a concrete selling price but doesn’t tell us anything about the markup or the mix of cost versus markup as a percentage of the total selling price. Two is insufficient on its own, and as we’ve seen in many other data sufficiency problems, what they’re trying to do here is fool us into thinking we need a specific price, a discrete value to get sufficiency. When the question stem is asking us only for a relative value and when we’re being asked for a relative value, a percentage, a fraction, a ratio be on the lookout for fooling yourself into thinking that you need an anchor point a specific discrete value.

I hope this helps. If you enjoyed this GMAT Markup Problem, try your hand at this Triangle DS Problem.

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Posted on
28
Jul 2021

GMAT Trade Show Problem – Data Sufficiency

GMAT Trade Show Problem Introduction

Today we’re going to take a look at the Trade Show Problem and this is a GMAT Data Sufficiency problem with averages as the focal point. But really the concept of average is distracting from this problem. So, if we take a look at the question stimulus, we want to figure out what we need, but we need to synthesize some of the information there to understand what we know.

We’re being asked whether or not it gets above a certain threshold an average of 90, and over six days that’s going to be over a total of 540 points. Notice how I did it mathematically, you can represent it graphically as a rectangle, but 90 times 6 is that 540 points. We know though that all of our days at a minimum are 80 which means we can build up from that piece of knowledge. We have 80 x 6 = 480 points and we want to know if we have more or less than 60 points above that minimum that we’re already working with that’s what we need.

Solving the GMAT Problem

Ways we might get it include any number of slices and dices for the performance of the rest of the days and the difficulty of this problem in large part will be dependent on how convoluted the GMAT gives us the introduced information on number one and two.

When we look at number one, we’re told that the final four days average out to a hundred. Once again, like with other average problems, each of the individual four days the performance doesn’t matter. We can just say each is exactly 100 and make that assumption, which means each is 20 over – we’re 80 points over the mean. Because we want to know whether we are more or less than 60 points, this knowledge that we’re 100 points tells us “Yes, definitively. We are over that average of 90, we’re over that surplus of 60 points.” So, number one is sufficient.

Number two gives us the opposite information, it talks about the minimum, and, in aggregate, that doesn’t let us know directly whether or not we make those 60 points. That is it’s possible but it’s also possible that we don’t, because we’re dealing with a minimum rather than a maximum or rather we’re dealing with information that can lie on either side of what we need. Therefore 2 is insufficient. Our answer here is A.

I hope that was useful. GMAT nation stay strong, keep averaging. You guys got this! I believe in you. If you want to test your GMAT Data Sufficiency skills, check out the Science Fair problem.

 

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Posted on
23
Apr 2021

Standard Deviation – Clustering (Birds) Problem

Hey guys! Today we’re going to take a look at a DS problem that is a skills problem, focused on GMAT standard deviation.

Standard Deviation & Variance

What they’re asking here is do we have enough information to compute a standard deviation? It’s useful to think of standard deviation as clustering. If we have a whole series of points we can define how clustered or un-clustered the group of points is. That’s all that’s standard deviation, that’s all that variance is. So if we have all the points that works. What we should be on the lookout here for are parametric measurements. Especially things like the average number is, because while the average can be used to compute standard deviation, we need to know how each of the points differs from the average. But if we have each of the points we always get the average. That is, we can compute the average. So the average is a nice looking piece of information that actually has little to no value here. So let’s jump into the introduced information.

Statement 1

Number 1 BOOM – tells us that the average number of eggs is 4 and that’s great except that it doesn’t tell us about the clustering. If we run some scenarios here we could have every nest have 4 eggs or we could have 5 nests have 0, 5 nests have 8, or 9 nests have 0, 1 nest has 40. These are all different clusterings and we could end up with anything in between those extremes as well. So number 1 is insufficient.

Statement 2

Number 2: tells us that each of the 10 bird’s nests has exactly 4 eggs. What does this mean? We have all 10 points. They happen to all be on the average, which means the standard deviation is 0. that is there’s no clustering whatsoever. But 2 gives us all the information we need so B – 2 alone is sufficient is the answer here.

Hope this was useful guys, check out the links below for a video about how to compute standard deviation as a refresher, as well as other problems related to this one. Thanks for watching we’ll see you again real soon

If you enjoyed this GMAT problem, try another one next: Normative Distribution

 

 

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Intro to GMAT data sufficiency article
Posted on
20
Apr 2021

Intro to GMAT Data Sufficiency- All you’ll need to know

By: Apex GMAT
Contributor: Altea Sulollari
Date: 20th April 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

Word problems

  • 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.

Memorize the answer choices

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:

A) Only statement 1
B)
Only statement 2
C) Both statements together
D) Either statement
E) 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 question: Number Theory: Data Sufficiency

 

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Posted on
10
Mar 2021

GMAT Ratio Problem – Mr. Smiths Class

GMAT Ratio DS Problem

Expressing Different Notations

Hey guys!

Expressing different notations is often challenging when you’re first starting out on the GMAT and by different notations mean percentages fractions decimals ratios. We learn all these separately and we tend to of them as separate systems of math when in fact they’re all different expressions of the same math. One half is no different from 0.5 is no different from 50 percent there are different ways of the same thing.

Breaking Down The Problem

In this problem all their testing is our ability to shift notations. We’re being asked what the ratio, keyword ratio, is between boys and girls in the or what do we need is just that a ratio it’s fairly straightforward. So they’re probably going to come to us with weird information that doesn’t quite look like a ratio. The big thing to note before we dive in is that when we’re being asked for a ratio. In fact, when we’re being asked for any sort of relative notation, fractions, percentages, anything that needs a base that is compared to a whole. We don’t need precise numbers.

Possible ways to solve this problem

So this leaves us open either to run scenarios if we want to or to deal entirely in the relative. So we’re looking for an expression of that ratio in a non-ratio sort of language. Number one tells us there are three times as many boys and girls. We can run a scenario with 3 boys, 1 girl, 75 boys, 25 girls, but we’re being given that ratio. It’s being expressed in language rather than with the term ratio or with the two dots : in between but it’s still a ratio. So it’s sufficient!

What Did You Miss?

Correction!! Number one states there are three times as many girls as there are boys. Why do we leave that error in? To point out that here it doesn’t matter. We’re not looking to determine whether the ratio is 1 boy to 3 girls or 3 girls to 1 boy or 3 boys to 1 girl. The only thing that matters, the threshold issue on this problem, is getting to a single specific ratio. What that is or in this case even reversing the boys and girls doesn’t matter because it’s a referendum on the type of information that we have. The moment we have a quantitative comparison of boys and girls coming from number one we know that number one is sufficient. Being able to have flexibility and even focus on the more abstract thing you’re looking for sometimes leads to careless errors on the details though and this is important. Many times those careless errors don’t matter, freeing yourself up to make those and understanding that you don’t have to manage the nitty-gritty once you have the big abstract understanding is very important.

Looking at Statement No. 2

Number two goes fractional, telling us that 1/4 of the total class is boys. We can break that into a ratio by understanding that a ratio compares parts to parts whereas a fraction is part of a whole so one out of four has a ratio of one to three. If this isn’t immediately obvious, imagine a pizza and cut it into four slices. One slice is one quarter of the total pizza the comparison of the one slice to the other three slices is the ratio one to three so if you get one slice and your friends get the other ones. The ratio of your slice to the others is 1:3. You have 1/4 of the total so two is also sufficient. Therefore, the answer choice here is D.

Hope this helped guys! Practice this skill of going in between these different notations because it’s one that pays off in dividends. Check out the links below for other problems and we’ll see you again real soon.

If you enjoyed this GMAT Ratio DS Problem, try your hand at this Triangle DS Problem.

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Intro to GMAT Data Sufficiency- All you’ll need to know
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

Word problems

  • 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.

Memorize the answer choices

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 practice question.

 

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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: 21st January, 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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