Quantitative Reasoning

what is the least common multiple of 6 and 8?

24

how many positive factors of 54 are odd

4

Even × Odd

= even

even + even

= even

odd + odd

= even

Odd × Odd

= odd

odd + even

= odd

even × even

=even

Area of a circle

A=πr²

Exponent Rules

(X^b)(Y^b) = (XY)^b (X^b/Y^b) = (X/Y)^b (X^n)(X^m) = X^n+m X^n/X^m = X^n-m

what is (sqrt(3) + 3sqrt(27))(2sqrt(3) - sprt(27))

-30

When integer a is divided by 5, the remainder is 2. when integer b is divided by 5, the remainder is 3. what is the remainder when a x b is divided by 5?

1 Numbers that leave a remainder of 2 when dovided by 5 are numbers 2 greater than a multiple of 5 (ex: 7). Those with a remainder of 3 will be three greater than a multiple of 5 (ex:8) Take 7×8 = 56. 56÷5 is 11 with a remainder of 1 true for all possible a and b values

what are the positive factors of 36?

1 2 3 4 6 9 12 18 36

exponent rules contd

1. Raising a negative number to an even power produces a positive result 2. Raising a negative number to an odd power gives a negative result

Adding/figuring rates of workers

1/total = 1/worker1 + 1/worker2 + 1/worker3 etc

what is the prime factorization of 210?

2 3 5 7

first 10 prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

what is the largest prime factor of 46,000

23

Multiply .029 by 10^3

29

Circumference of a circle

2πr

Area of a cylinder

2πr^2 + 2πrh

prime number

A whole number that has exactly two factors, 1 and itself.

Simplifying Radicals

If the number inside radical is a multiple of a perfect square, expression can be simplified by factoring out perfect square sqrt(20) = sqrt(4*5) = 2 sqrt (5)

30-60-90 Triangle Theorem

In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg, and the longest leg is √3 times as long as the shorter leg

simple interest

Interest earned only on the original principal amount invested

Dividing fractions

Invert (reciprocal) the second fraction and multiply

Multiplication amd Division of Radicals

Multiply or Divide the numbers outside the radical signs, then the numbers inside

Addition and Subtraction of Radicals

Only like radicals can be added to or subtracted from one another.

p( A or B)

P(A) + P(B) - P(A and B)

least common multiple

The smallest multiple (other than zero) that two or more numbers have in common.

Improper Fraction

a fraction whose numerator is larger than the denominator

Mixed Number

a number made up of a whole number and a fraction

prime factorization

a number written as the product of its prime factors

If -1<x<1 but x is not zero, which has the greater value: absv(x^4) or absv(x^5)

absv(x^4) answer must be a fraction fractions absolute value decreases as they are raised to higher powers

Factor

aka Divisor, positive and negative integers by which it is evenly divisible, no remainders

Even numbers are:

evenly divisible by 2

compound interest

interest earned on both the principal amount and any interest already earned

the combination formula

n! / (k!)(n-k)! where n is group as a whole and k is number in subgroup formed

what is the largest 4 digit multiple of 71?

the largest 4 digit number is 9,999. divide 9,999 by 71 and get 140 with remainder of 59. 9,999 is 59 greater than the largest common multiple

formula for overlapping sets

total = group A + group B - both + neither