Algebra for GMAT
What I discovered using the 2005 edition of “Cracking the GMAT” (The Princeton Review) was that algebra problems can be solved without using algebra, but an easier method: plugging in.
Basically you just replace with number the unknown data represented with letters. Sounds stupid, but it works and you gain time.
Plugging in a number in the question:
- Pick one or more numbers to replace the letters in the problem (question)
- Using your numbers, find an answer to the problem
- Plug your numbers into the answer choices to see which choice equals the answer you found in step 2
Plugging in a number in the answers:
- Always start with answer C. Plug that number into the problem and check if it gives you a solution.
- If choice C is too small, choose the next larger number
- If choice C is too big choose the next smaller number
If the question contains “must be”, “could be” or “cannot be”, the problems can be solved by plugging in but you may need to plug more than one number.
You must have at least as many distinct equations as you have variables for the equation to be solvable.
ax² + bx + c = 0
x = [-b +/- √ (b²-4ac)] / 2a
Also, simultaneous equation can be solved an addition or subtraction of one equation from the other. This way you can eliminate one of the unknowns.
GMAT’ “most wanted”:
- (x + y) ² = x² + 2xy + y²
- (x + y)(x – y) = x² – y²
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:
- one side, one time 1/6
- two sides, one time 2/6
- one side, both times 1/6 x 1/6 = 1/36
- one side or another chosen first 1/6 + 1/6 = 2/6 = 1/3
- the odds that one side does not happen 5/6
- 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) … x3x2x1
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.
Basic Arithmetic for GMAT
The math problems at GMAT are basic from 3 areas: Arithmetic, Algebra and Geometry.
Basic arithmetic operations:
- addition (8+8)
- subtraction (8-4)
- multiplication (8×3)
- division (8/2)
- raising to a power
- finding a square root
Fraction: x/y (part/whole) x = numerator, y = denominator.
Decimals are in English indicated by a point.
Ratio: The whole in ratio is sum of all parts. If ratio is a fraction the whole is the sum of the numerator and the denominator.
Average = total sum of the items/total number of the items.
Arithmetic mean = the process of finding an average.
How to find the Median:
- first order the numbers from least to greatest
- if n is odd, median is the middle number
- if n is even, median is the average of the 2 middle numbers
Mode = the number or the numbers that occur most frequently in a list of numbers.
Range = the greatest value in the numerical data minus the least value.
Standard deviation = measures the distance between the arithmetic mean and the set of numbers.
- first, find the differences between that average and each one of the set of numbers and square each of the differences
- second, find the average of the squared differences and take the square root of this average
Frequency distribution: if a,b,c = numbers, f = frequency, av = average.
Standard deviation = √ {[(a-av) ² x f + (b-av) ² x f + (c-av) ² x f]/n.}
Exponents – multiplying, dividing, raising a power to a power, distributing.
In a percentage increase or decrease problem, you must put the amount of the increase or decrease over the original amount.
In compound interest problems, the answer will always be a larger number than it would be in a similar simple interest problem.
