Alright, you’ve been studying the GMAT basics. You understand what is really being tested along with the problem types, methods, and strategies. You’ve even memorized all the basic formulas and taken a dive into some of the more challenging content areas. So what’s next? That’s simple, practice…over and over and over again. If you do this, you are likely to start hitting tough probability questions at some point. Along with combinations and permutations, this is a content area that the GMAT can use to up the degree of difficulty quite a bit. So let’s take a look at a tough probability question and break it down:
A fair coin is tossed five times. What is the probability that it lands heads up at least twice?
The key to solving this is the phrase ‘at least twice.’ This means that … Read full post
Take a look at the picture with this blog. It’s an iconic optical illusion. Stare at it—what do you see? The picture is called the Great Wave off Kanagawa, painted by Katsushika Hokusai, a Japanese artist famed for his brilliant compositions. This drawing is of a wave, of course, but do you see the other wave, the reverse wave in the sky?
This image utilizes negative space. You take the whole frame, the great big rectangle, you block out that actual image—and what remains is, in its own right, an interesting picture.
To find the area of the shaded region, we need to subtract the area of the smaller inner circle from the large outer circle—the difference is the area of the ring.
But the concept extends beyond … Read full post
Tackling some of the tougher GMAT probability questions efficiently relies on both steady practice and your ability to make two key decisions well. First, you will need to quickly and accurately assess the total number of possible outcomes (the denominator of your probability equation). Second, within a multitude of possible approaches, you will need to determine the most efficient route to calculate the number of desired outcomes (the numerator of your probability equation).
With the clock ticking away on your GMAT CAT, figuring out the total number of possibilities can be time-consuming and fraught with room for error. For instance, if a question asks about the probability of getting at least 2 heads on 5 coin tosses, you could sit there all day writing out possibilities:
So forth and so on. I know I got dizzy with the possibilities just writing those three out. There is … 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
Piecing together the time to study for the GMAT can be challenging. In today’s blog, I’m going to talk about three students (whose names I’m changing to protect their identities). Each had a major obstacle to studying, and each overcame it in a different way. I hope these students’ examples can help some of you reach your GMAT and MBA goals.
Case Study 1: Vincent, the Entrepreneur
The Challenge: Vincent was a busy man when I was tutoring him. His schedule was very flexible—his main source of income was a business that he started and ran himself—but he was distracted at all hours by emails and phone calls related to his work.
The Solution: Vincent needed a time and place where he could study in peace.
Because of his flexible work schedule, it was easier for Vincent to find time than it is for some other students. He … Read full post
While my students certainly accept that they have to take the GMAT, I often hear complaints about the applicability of GMAT topics – especially math – to real world situations. My usual response to this observation is that the GMAT is using math questions to test critical thinking skills that business schools consider essential.
However, some GMAT problems have surprising real world applications outside the realm of business. The sample problem below is an example of one such question. Specifically, it can help you win at craps.
If you want to try the problem on your own, skip down to it now and then return here – part of this discussion will give you clues about the correct answer.
For those of you not familiar with craps, the basic play is fairly straightforward. You roll two dice and if the sum of the result on each die is 7 … Read full post