Quantitative - Problem Solving Flashcards
How do you factor using “the third recycled quad?”
A squared minus B squared
(A minus B ) X (A plus B)
What is the distinction between a set and a sample space?
Set = Group of objects
Sample Space = All the relevant objects from which it is possible to select a set.
What is a “complementary set”?
When set B is defined within a sample space, all members of the sample space that are not members of B are in the complementary set.
A good test for a complementary set is to ask the question “Can the sample space include any more options besides A and B?”
Define a subset.
If all members of set B are also members of set A, set B is a subset of A.
The prime factors of any integer that is the power of another integer come in pairs, triplets etc. according to the power.
If a is an integer and a squared is an integer, the prime factors of a squared must come in pairs.
What is the division operation and what are the parts?
Dividend / Divisor = Quotient
What is the one odd/even rule of fractions?
And odd integer divided by an even integer will always be a fraction.
Odd / Even = Fraction
Multiples rules for addition
1) multiple of n + multiple of n = Must be a multiple of n
2) multiple of n + NOT multiple of n = cannot be multiple of n
3 NOT multiple of n + NOT multiple of n = maybe a multiple of n
If the dividend is even and the divisor is odd, the quotient must be what (odd or even) when the remainder is zero
Even.
Even x odd = even
means
Even = even / odd
What are dozen F numbers
Different (odd/even, primes, multiples, positive/negative) One Zero Equal number for different variables Negatives Fractions
What is the workflow for LCM problems?
Least common multiple problems can be approached as follows:
1) find the prime factors of all the numbers in the question.
2
What is the workflow for solving simultaneous equations?
Stack em vertically
Manipulate if necessary to cancel out variables you don’t need.
Add or subtract to get a one-variable equation
What is the workflow for inequalities involving absolute value that take the form:
|something| number
Example: |x-6|
Consider two scenarios
1st - copy the inequality without the absolute value brackets and solve
2nd - remove the brackets, put a negative sign on the other side of the inequality AND flip the sign
Then combine into a single statement of range, eg 4
Method for factoring a quadratic.
In (x+e)(x+f) the 1) first task is to find e and f. They must meet the following conditions:
1- their product is equal to c
2- their sum is equal to b
2) wrote them in their appropriate places in factorized form.
3) the equation is now the product of two factors. Since the product is zero at least one of the factors is zero. Set each factor individually to zero and solve for x. These are the solutions to the quadratic.
