It’s finally time! You’ve waited all weekend for it, and we’re finally going to share the solution, and more importantly, helpful tips for dealing with GMAT Roman Numeral questions. If you didn’t see Friday’s practice question, take a look now:
GMAT Problem Solving
Roman Numeral Question
If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y is even
III. xz is even
- A) I only
- B) II only
- C) III only
- D) I and II only
- E) I, II, and III
Strategy and Tips for Solving GMAT Roman Numeral Questions
For Roman Numeral questions, start by finding the statement that appears most often in the answer choices, and evaluate it first. Therefore, if it is untrue, you can eliminate the highest number of answer choices.
In this case, … Read full post
Yesterday, we posted a GMAT practice question on Facebook. It got a lot of attention and many responses. Here it is again:
Our Facebook audience mostly answered A, with a few votes for D. The correct answer is indeed A, and here’s why…
- Statement (1) is exactly what is needed – it gives you a precise value for . Statement (1) is sufficient, so eliminate answer choices C and E.
- Statement (2) alone, however, leads to two possible values for b, because you’d have to substitute the square roots of 25 for a, and those square roots are BOTH positive AND negative 5 (remember this! The GMAT likes to
Did you try out Friday’s GMAT problem solving practice question? If not, give it a try before you look at the solution. Here’s a reminder:
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
- (A) 90
- (B) 110
- (C) 120
- (D) 130
- (E) 220
The first step in this problem is to translate the word problem into math. You can write two equations based on the information in the question stem. Call the balcony seats B and the orchestra seats R (avoid using the letter O as a variable because it looks like the number 0.) Now, you can write one equation based on the number … Read full post
Did you try out our GMAT Data Sufficiency practice question? If not, take a couple minutes now to give it a try before reviewing the explanation.
Now, let’s get down to brass tacks on the Geometry and DS skills you need to solve this one…
One way to find the area of a quadrilateral is to divide it into triangles and add the areas of the triangles, which can be found using the formula for the area of a triangle: (1/2)(Base)(Height).
If you add dashed lines to the diagram connecting points A and C and points B and D, you will see that the quadrilateral is composed of 4 right triangles:
You can see that one side of each triangle is a radius of one of the circles; for example, AB is a radius of circle A and is the hypotenuse of triangle ABE. Also, you’ll notice that triangles … Read full post
Translating word problems into algebra is a staple skill of GMAT test-takers, one that underlies countless problems in practice and on Test Day. But some challenging translations occur as part of probability and combinatorics problems. That’s because a pair of the most basic words in the English language, “And” and “Or,” suddenly become overburdened with mathematical significance.
“And” is the simpler of the two. When “And” represents independent choices—cases in which one option or arrangement has no impact on the other choice—just multiply the outcomes. For instance:
“The number of ways to purchase three board games and two video games” is an independent choice. The board games we pick have no impact on the video games we pick. So, to translate: [The number of ways to purchase three board games] × [the number of ways to select two video games]. Of course, we’d need the combination formula … Read full post
Mixture problems show up frequently on the quantitative section of the GMAT and fall into two basic categories. As each type of mixture question will be approached in fairly different ways, it is important that you know the difference between them.
First, there are mixture problems that ask you to alter the proportions of a single mixture. These questions could, for example, tell you that you have a 200 liter mixture that is 90% water and 10% bleach and ask how much water you would need to add to make it 5% bleach. The key in this type of question is the part of the mixture that is constant – in this case the bleach. While we are adding water, the amount of bleach stays the same. First, determine how much bleach we have. 10% of 200 is 20 liters. Next, we know we want those 20 liters to equal … Read full post
Mastering ratio questions on the GMAT requires systematic organization of the individual pieces and a solid understanding of how ratios are typically presented and tested on test day. One of the most common presentations of ratios on test day is a question that presents a part:part or part:whole relationship and asks for the actual number of a part, the whole, or a difference between the parts.
The first thing to note about ratios is that they represent relationships between items. On the GMAT Quantitative Section, the ratio is usually in the simplest form; I call this multiple level 1 because it represents the smallest potential positive quantity for each aspect of the ratio. For instance, if a question tells you that the ratio of apples to oranges is 2:3, you know immediately that the minimum number of apples possible is 2 while the minimum number of oranges is … Read full post
In my years of teaching, I’ve seen all kinds of clever solutions to GMAT math problems. I’ve also seen all kinds of errors. Some are utterly bizarre—and fortunately, seldom repeated, because the students who make those mistakes usually face-palm when they review their tests and go on to learn from their missteps. But some errors are so common and so often repeated that they earned their own names. One such example is the “fencepost error.”
Here’s a simple example: Say we are setting up a straight fence that’s exactly 100 ft long, with posts every 10 feet. How many posts do we need?
Did you say 10? Tempting, but that’s the right answer to the wrong question. There are 10 sections of fence, each 10 feet long. But there are actually 11 fenceposts, because you start with a fencepost, at 0 feet!
This error can trap the … Read full post
Imagine you are driving from Chicago to Los Angeles, and you want to know what your average speed needs to be to reach Los Angeles in a certain number of hours. You would probably start by determining the speed you will be able travel during certain parts of your journey. Since most of the distance will be covered by highway, you might plan to travel most of the distance at 70 miles per hour. However, you will also want to plan for some traffic when you are still in or near Chicago and when you get close to Los Angeles. During these parts of your journey let’s say you can plan to travel at 30 miles per hour.
When calculating the average speed at which you will be traveling, you need to avoid the trap of just averaging these speeds together and planning on an average speed of 50 miles … Read full post
Ever since I started teaching GMAT classes, I have taken note of any references to standardized tests I come across in television shows and movies. In the six years of doing so, I have found that these references almost always follow the same pattern. One of the characters needs to take a standardized test that they find difficult or boring. In order to illustrate this to the other characters, they will read an example of one of the questions on the exam. Invariably, the question they read involves two trains leaving two different stations at two different times and traveling towards each other.
Because of this, rate problems that feature two trains (or cars or people or anything else) have a bit of a bum rap. These questions are seen, unjustly, as difficult, time consuming and complicated. However, by learning only a few basic rules, you can handle these … Read full post