Quant Flashcards
Least Common Denominator (LCD)
List the multiples of the numbers to get the LCD.
5 - 5, 10, 15, 20, 25, 30
6 - 6, 12, 18, 24, 30
LCD is 30
Comparing Fractions
- Reference point (bigger than one half, smaller than one half)
- Bow tie method
- Common denominator
- Common numerator (the bigger the denominator, the smaller the fraction)
Base Fractions and their Decimal & Percentage Approximations
1/2 - 0.5 1/3 - 0.333 1/4 - 0.25 1/5 - 0.2 1/5 - 0.167 1/7 - 0.143 1/8 - 0.125 1/9 - 0.111 1/10 - 0.1
Fractions & their decimals - more complex ones
5/6 - 0.833
3/7 - 0.42
4/7 - 0.571
5/7 - 0.714
6/7 - 0.857
5/8 - 0.625
7/8 - 0.875
Quadratic Identities
(1) (x+y)^2 = (x+y)(x+y)= x^2 + y^2 +2xy
(2) (x-y)^2 = (x-y)(x-y) = x^2+y^2-2xy
(3) (x+y)(x-y) = x^2-y^2
Integer
A number that can be written without a decimal or a fractional component
Is zero positive or negative?
Neither
Whole number
Nonnegative integer. That is - positive integers and the number zero
Zero properties
`1 - Zero x any number = zero
2 - Zero / any number = zero
3 - Any number / zero = undefined
4 - Square root of zero = zero
5 - Zero raised to any positive power = zero (0^0 is undefined and never on the GMAT)
6 - Zero is neither positive nor negative
7 - Zero is the only number equal to its opposite (0 = -0)
8 - Zero is a multiple of all numbers
9 - Zero is the only number equal to all of its multiples
10 - Zero is not a factor of any number except itself
11 - Any number to the power of zero = 1
12 - Zero is even
13 - Zero can be added or subtracted from any number without changing the value of the number
One properties
1 - One is a factor of all numbers, and all numbers are multiples of 1
2 - One raised to any power is 1
3 - Multiplying or dividing any number by 1 does not change the number
4 - One is an odd number
5 - One is the number with exactly 1 factor
6 - One is not a prime number (the first prime number is 2)
Sums and Differences of odd & evens
Even +- Even = Even
Odd +- Odd = Even
Even +- Odd = Odd
Odd =- Even = Odd
Multiplication rule for evens and odds
Even x Even = Even
Even x Odd = Even
Odd x Even = Even
Odd x Odd = Odd
Division rules for events and odds
Even/even = odd or even
even/odd = even
odd/odd = odd
odd/even - is not possible
Absolute Value
Distance of the number from zero on the number line
Prime numbers less than 10
2, 3, 5, 7
Prime numbers less than 20
11, 13, 17, 19
Prime numbers less than 30
23, 29
Prime numbers less than 40
31, 37
Prime numbers less than 50
41, 43, 47
Prime numbers less than 60
53, 59
Prime numbers less than 70
61, 67
Prime numbers less than 80
71, 73, 79
Prime numbers less than 100
83, 89, 97
Remainder Equations
x/y = Q + r
x=QY+r
Q= (x-r)/y
r = x-Qy
Patters in Units digits when a positive integer is raised to consecutive powers.
0 > 0
1 > 1
2 > 2-4-8-6
3 > 3-9-7-1
4 > 4 (odds) - 6 (evens)
5 > 5
6 > 6
7 > 7-9-3-1
8 > 8-4-2-6
9 > 9 (odd) - 1 (even)
The product of n consecutive even integers is divisible by…
2^n * n
Root of X^2 =
Absolute value of X
Even root of any number X will equal absolute value of x.
non negative perfect cubes
0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
Radicals (square roots of non perfect #s) - 1 to 8
sq root 2 = 1.4 sq root 3 = 1.7 sq root 5 = 2.2 sq root 6 = 2.4 sq root 7 = 2.6 sq root 8 = 2.8
2^n + 2^n = 2^n+1
Exponents rule - If 0 < x < 1, then…
x^2 < x < sq root of x
Never multiple or divide an inequality by a variable unless the sign of the variable is known
Simple Interest
Principal x Rate x Time
Principal - initial amount of money that was borrowed, lent, or invested
Rate - simple interest rate expressed as a decimal (or fraction)
Time - duration of loan or investment
Units of rate & time must match.
If interest rate is annual and time is 8 months - it should be added to the equation as 8/12 (and not “8”)
If interest rate is expressed as a variable - it should be added to the equation as x/100
Interest earned in any period on the principal invested is not factored into future amounts of interest earned.
Inverse Variation
y = k/x
Direct varation y=kx
Percent Change
((Final value-initial value)/Initial value)*100
