Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!
The tens digit of
is
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We’re happy to introduce the Knewton Weekly Math Challenge. Every Wednesday we’ll post a very difficult quant question. The first person to answer correctly in the comment field below will win the new Knewton T-shirt. After the right answer appears in the comments (you can only post one answer, and you must explain how you arrived at your answer — so take your time), we’ll post a full explanation. Here’s the first question. Good luck!
In a certain game, a player begins with a bag containing tiles numbered 1 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!
A circle is inscribed in an equilateral triangle, such that the two figures touch at exactly 3 points, one on each side of the triangle. Which of the following is closest to the percent of the area of the triangle that lies within the circle?
There are two types of interest problems on the GMAT, and they include simple interest and compound interest. Simple interest is the most basic and is a function of P, the principle amount of money invested, the interest rate earned on the principle, i, and the amount of time the money is invested, t (this is usually stated in periods, such as years or months). The resulting equation is:
The GMAT is notorious for many reasons. As you continue to study with relevant books and materials, you’ll find that one aspect of the test will continue to frustrate you – getting the correct answer, but not answering the right question.
One of my students asked me what I think are the three most important things in preparation for the GMAT. I said that the most important is knowing what the question is asking, the second most important was knowing where you are starting.
The third most important thing, and the topic of today’s article, is to know all of your equations and formulas. By knowing them, I mean knowing them really well and more than just being able to recite them. Understand when to use them and when not to use them.
Let me give you an example:
Last week, we took a look at how to analyze a Critical Reasoning question. This week, we’re going to do the same with a Problem Solving question. The GMATPrep® problem we’re using this week is one that we’ve already discussed how to solve in a previous article; click here to read that article and try the problem first.
Here’s the problem again; if you didn’t read the first article and try the problem already, then try this problem now:
The most difficult GMAT Quant questions often have nothing to do with setting up equations for triangles or finding how many different arrangements you can make of a group of people standing in a line. Often, the most difficult GMAT Quant question in a seemingly innocuous form:
Is x an integer? Is b even? Which of the following must be positive?
Integers seem so harmless! But within the broad scope of integers, let’s look at a few key concepts about integers that you’ll need to know to beat the GMAT:
For me, one of the most exciting parts of Kaplan’s new GMAT revision for 2010 is its emphasis on Identifying the Task in Quantitative Problem Solving questions. Often, Problem Solving questions give a test-taker a large amount of information—sometimes as much as five or six equations’ worth—and when the pressure is on and the clock is ticking, it can be tough to get this information organized enough to answer the question, not to mention the amount of time that can be lost in doing so.
One of the most efficient ways of zeroing in on the answer in complicated questions is to use what I call a “master equation.”
While recuperating from Arthroscopic knee surgery, I decided to write a piece on Data Sufficiency questions. Then I visited the website and saw that Ben Leff had done something on that just a few days ago.* I decided to alter the focus a bit and talk more generally about the nature of the point he was making and expand to talk about the distinctions between Data Sufficiency (DS) and Multiple Choice (MC) questions, with most of the focus on the DS questions.
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!
If 1/(x – 2) = 1/(x + 2) + 1/(x – 1), which of the following is a possible value of x?
Let’s back up a bit and think about the different algebraic equations that you’ll see on the GMAT. The GMAT tests two basic equations: Linear Equations and Binomial Equations. I’m sure through your current GMAT studying, you’ve run into the concept of linear equations – linear is easy to remember because it means ‘line’. All linear equations are straight lines.
Binomials are not straight lines. In the traditional linear equation, a variable is raised to the first power (or, if it simply the variable ‘x’). Whenever you ‘square’ a variable, you have a binomial equation.
Sets, matrices and Venn Diagram – they are all the same. It’s really a matter of preference; some students like to use Venn diagrams, and others make matrices. Personally, I prefer a matrix format, but there is no “better” way.
On your GMAT, you will encounter 1-3 questions that contain overlapping groups with specific characteristics. You will almost never see more than two characteristics (since you can’t draw 3D on your scratch paper). For illustration, let’s take a look at the following Data Sufficiency example:
Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 750+ level question, so do not worry if you cannot solve the problem in a 2 minute time frame. If you are up for the challenge, however, set your timer for 2 minutes and go!
Two positive numbers differ by 12 and their reciprocals differ by 4/5. What is their product?
