GMAT Quantitative: Probability and Geometry

by Oren Lahav

Quantitative Section Made Easy: Probability and Geometry Review
Here we cover material that will show up in the Quantitative Section of your GMAT, so if you want to do well on your GMAT and get into that MBA program, you better review this stuff. In this lesson we move on to slightly more advanced topics, such as Probability and Combinatorics, as well as Geometry.

Â» Start off with Probability Concepts

Probability outlines the likelihood of something happening out of all of the possible outcomes. For example, rolling any certain number in a die has a probability of 1/6 - since there are 6 sides but we only care about 1 number.

The probability of something not happening is: 1-p

Where is the probability of the same thing happening. The total probability of all outcomes always sum up to 1.

The probability of outcome a or outcomes b is: a+b

The probability of outcome a and outcome b is: a * b

The only trick is to add up all the possibilities that result in a certain outcome happening, and divide by the total options you have.

Â» Combinatorics also play a part here

Counting events is simple to do. Say there are 3 possibilities for event A, and 2 for event B. The total possibilities in terms of both events are:

3 * 2=6

Since we have 2 option in B per option in A. Counting orders is a bit different, but just remember that there are: n!=n * (n-1)... * 2 * 1 ways to order n elements.

If we're selecting r out of n elements and order matters, we're using permutation. The formula is:

$\frac{n ! }{(n-r) ! }=n(n-1)...(n-r+1)$

On the other hand, if order doesn't matter, you divide the whole thing by the number of ways to order the r elements, giving you: $\frac{n ! }{(n-r) ! r ! }$

Note: If you are not comfortable with probability or combinatorics, don't stress out, these topics aren't prominent on the GMAT. However, while memorizing the permutation formula isn't necessary, you should know how to deal with this sort of question when it hits you. A more in-depth combinatoric lesson is right here, and a simple probability lesson can help you figure things out.

Â» Finally, some Geometrical Concepts

Here's a list of simple concepts you should be aware of for the geometry problems:

Angles. Two angles lying on one line always add up to 180 degrees. opposite angles in the intersection of 2 lines are always equal. Similar (and opposite) angles between two parallel lines cut by the same line are equal as well.

Triangles. The angles in a triangle add up to 180 degrees. If the triangle is equilateral, all sides are equal and all angles are 60. If the triangle is isosceles, two sides and the two angles opposite those sides are equal. If the triangle is right, it's got one 90 degree angle, and in that case the Pythagorean Theorem applies - the square of the hypotenuse (long side) equals the sum of the squares of the other two sides. Area of a triangle is always: $\frac{bh}{2}$

Circles. area of a circle is $\pi r^2$ and the circumference is $2\pi r$ , if r is the radius, which is also half of the diameter. Inscribed triangles in a circle that have one side as the diameter are always right-angled, and tangents touching the circle at one point only are always perpendicular to the radius at that point.%

Rectangles other shapes, 3-D Solids. all of these are easy to deal with if you know them. Other than very simple rectangular prisms you'll be given volume and surface area formulas.

Analytic geometry. involves a coordinate grid, lines, their equations and slopes.

For a more thorough review of these topics, look here for Geometry and Analytic Geometry.

Â» A few Final Notes

Remember a few thing. First, there are no calculators allowed, so you won't need one. Thus, the probability and geometry questions will only involve nice fractions and small, simple numbers. Also note that the portion of the GMAT that contains these questions is fairly small, since this material is not highly applicable to everyday business functions. Don't stress out too much over these, and once you're ok with it move on to the next lesson, which will deal with those Data-Sufficiency problems.

Â» Additional GMAT Lessons

Â»Â» Quantitative: Problem Solving I

Â»Â» Quantitative: Data Sufficiency

Â»Â» Quantitative: Strategies

Â»Â» Quantitative: More Strategies