Featured Video Play Icon
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’ll 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.

Read more
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: 28 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.

 

Read more
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

Read more