Try this advanced GMAT probability question, testing your knowledge of the ins and outs of how probability works.
The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A and B occurs is 0.94. What is the probability that event B occurs?
In order to find the probability that event B occurs in this problem, we need to set up and equation that includes the probabilities we are given and allows us to solve for B. We are told that the probability that at least one of A or B occurring is 0.94. ‘At least one of A or B’ means that an outcome is desired if A occurs and B does not, B occurs and A does not or A and … Read full post
What should you do when you see a GMAT problem asking you for the average rate over an entire journey? Try your hand at this problem and let’s see.
A canoeist paddled upstream at 10 meters per minute, turned around, and drifted downstream at 15 meters per minute. If the distance traveled in each direction was the same, and the time spent turning the canoe around was negligible, what was the canoeist’s average speed over the course of the journey, in meters per minute?
In average rate problems many students forget that average rate means total distance divided by total time and not the average of the rates. This is especially true on problems, such as this one, that give the test-taker two rates, but no distances and no times. When this occurs, the most concrete strategy, … Read full post
Knowing how to use the distance = rate x time formula in various permutations will help you tremendously on the classic GMAT speed word problems. Just remember that when asked about average rate over an entire journey, you must think about total distance and total time over that journey….
A car drove from Town A to Town B without stopping. The car traveled the first 40 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 120 miles if the car’s average speed for the entire trip was 40 miles per hour?
To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey, and is not the average of the speeds. … Read full post
As you may have noticed in prepping for the GMAT, in many cases the challenges you face in GMAT problems are less about the specific math skills, and more about translating word problems into mathematical equations in a fast and efficient way. Figuring out quickly HOW to approach the problem is one of the key skills the GMAT is testing (and, incidentally, a key skill in the business world as well). Try this typical word problem translation question, and be sure to practice GMAT-style word problems frequently, in addition to just practicing algebraic skills.
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
The first step to answering this question is translating the information in the … Read full post
As you have studied for the GMAT, you have probably heard over and over again that you need to make sure not to fall for trap answers. In no type of question is this truer than in quantitative questions asking about average rates.
When you encounter an average rate question you must immediately remind yourself that average rate means the total distance divided by the total time; it does not mean the average of the two rates. You can be assured that an answer choice that simply averages the two rates you have been given will be listed (this is the trap!), so make sure you always keep the definition of average rate in mind.
When you see these problems, use the rates you have been told in the problem, along with any other information you have, to calculate the total distance traveled, and the total … Read full post
Try your hand at this sample GMAT problem focusing on a specific probability situation.
Each person in Room A is a student, and 1/6 of the students in Room A are seniors. Each person in Room B is a student, and 5/7 of the students in Room B are seniors. If 1 student is chosen at random from Room A and 1 student is chosen at random from Room B, what is the probability that exactly 1 of the students chosen is a senior?
In this problem we are asked to determine the probability of choosing exactly 1 senior. To be more specific, this means that we will need to select 1 senior and 1 non-senior.
There are two ways this can be done. We can select a senior from Room A and a non-senior … Read full post
We invite you to give our GMAT Combinations Challenge question below a try! Aim for about 2 minutes and give it your best shot before reviewing the answer & explanation. Good luck!
Jane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Jane or Thomas is to be selected?
The first step in this problem is to recognize that order does not matter. We must create a committee of four people, but we are not putting these people in any sort of order. Because order does not matter, we must use the combinations formula, which is n!/[k!(n-k)!], in order to determine the number of possible outcomes.
However, … Read full post
The last time we looked at GMAT rate problems dealing with two trains, we discussed how to identify the correct strategy for a particular problem. Now we are going to take this a step further and look at an example of a GMAT quantitative problem in which these strategies can be implemented.
Let’s consider the following:
City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:30 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
In order to solve the above problem, we first must get the trains to leave at the same time. Train D leaves 30 minutes after train C, so we must find out how far train … Read full post
Before students begin studying for the GMAT – before they even know anything about it beyond that it tests math and verbal – one question type worries students more than any other: a question about two trains traveling on parallel tracks.
Every time I start to go over a question about two trains, two cars or, in one rather quirky problem, two earthworms, students roll their eyes and prepare for the worst.
But these problems have received a bad rap. In order to solve them, students only need to be able to remember the basic rates formula, learn a two-step method and be able to differentiate between the two flavors in which this problem appears.
Learn the Rate Formula
First up, the rate formula. A rate is just something per something. It can be dollars per jobs, people per team or any other ratio. However, the most common rate … Read full post
When a straightforward arithmetic problem appears on the GMAT, many test-takers treat it as a break from the more complicated problems that are on the GMAT. While arithmetic problems are often not as complicated as many of the other problems on the test, you should still be careful not to make careless math errors. The most common cause of such errors is a mistake in the order of operations.
Operations in an arithmetic problem need to be completed in a specific order. The best way to remember is via the acronym PEMDAS, which stands for parentheses, exponents, multiplication, division, addition and subtraction. Regardless of the actual order of the operations listed in the problem, they should always be completed in this order.
PEMDAS in Action
To see why order of operations is so important, let’s consider the following two expressions:
(5 – … Read full post