Arithmetic for GMAT

The arithmetic for GMAT is simple, as is practically everything about GMAT.
Attention: Simple does not mean easy! It is not easy because you have the TIME constraint and your own pride.
We all make the mistake of paying less attention to something because is easy. I am not saying to you have to pay more attention to the problems. The GMAT problems are not THE PROBLEM. TIME is THE PROBLEM.
Remember the formulas and practice with them until they become a reflex. But pay attention to your own ego, that will whisper in your year “I can do this problem too”. When you feel that is taking you too much time, and this means ONE MINUTE, click a random answer and move on!

Now, arithmetic:

1.Rate x Time problems: The only formula you need is rate x time = distance         r x t = d

2. Work problems: ALWAYS think of how much of the job can be done in one hour.

3. Mix problems:

Interest = principal x interest rate x time.
Discount = if a price is discounted by n percent, the price becomes 100-n percent of the original price.|
Profit = revenues minus expenses = selling price minus cost.

4. Functions:

The strange character * or # is part of a fix unit not a formula. What you replace with numbers are letters like x or y.
Domain = the set of all allowable inputs for a function.
Sequence = a function defined only for input values that are the positive integers and possibly 0.

5. Probability.

An event is a particular set of outcomes.
Numerator = the number of possibilities that match what you want.
Denominator = the total number of possibilities.

Six-sided die:

1. one side, one time 1/6
2. two sides, one time 2/6
3. one side, both times 1/6 x 1/6 = 1/36
4. one side or another chosen first 1/6 + 1/6 = 2/6 = 1/3
5. the odds that one side does not happen 5/6
6. the odds that at least one side will happen 1- 5/6 = 1/6

6. Permutations and Combination.

Different source, order does not matters:

• When a problem ask you to choose a number of items to fill specific spots and each spot is filled from a different source, all you multiply the number of choices for each of the spots.

Single source, order matters:

• When a problem asks you to choose from the same source to fill specific spots, you multiply the number of choices for each of the spots. Attention: the number of choices keeps getting smaller. n! = n(n-1)(n-2) … x3×2x1

Single source, order matters but only for a selection:                An/k = n!/(n-k)!

Single source, order does not matters:       C n/k = n!/k!(n-k)!

7. Sets

Set = collection of numbers (elements) or other objects.
T = {1, 2 , 3, 4, 5}                   S = {1, 2, 3}.
|S| = 3 (number of elements).
S = subset of T

Union S U T = {1, 2 , 3, 4, 5}.
Intersection S ∩ T = {1, 2, 3}.
Disjoint or mutually exclusive = no elements in common.

Venn diagrams = google! :)
|S U T| = |S| + |T| – |S ∩ T|
If S and T are disjoint then |S U T| = |S| + |T| since |S ∩ T| = 0.