Number Sense Flashcards
Divisible by 3
Divisible by 3 is fhte sum of the digits is divisible by 3
Divisible by 9
Divisible by 9 is fhte sum of the digits is divisible by 9
Multiply a decimal with a big number
Trade decimal spaces 50,000 x .007 = 50 x 7
When multiply or divide by a negative the answer is?
negative
Prime
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101
Powers of 2
21=2; 22=4; 23=8; 24=16; 25=32; 26=64; 27=127; 28=256; 29=512; 210=1024
Powers of 3
31=3; 32=9; 33=27; 34=81
Powers of 4
42=16; 43=64
Powers of 5
52=25; 53=125; 54=625
Square roots
32=9; 42=16; 52=25; 62=36; 72=49; 82=64; 92=81; 102=100; 112=121; 122=144; 132=169; 142=196; 152=225
negativeODD
Negative number
negativeEVEN
Positive number
Y-3
Y-3 = 1/y3
Ab x Ac =
Ab x Ac = Ab+c
X0 =
X0 = 1
(Xa)b =
(Xa)b = Xab
ab/ ac =
ab/ ac = a b-c
Cube Roots
3, 4, 5
33 = 27; 43 = 64; 53 = 125
Square Roots (bigger)
132 =169; 142=196; 152=225; 202 =400; 252=625; 302 = 900
a-b =
a-b = 1/ab
√ab =
√ab = √a x √b
√a/b =
√a/b = √a / √b
√a =
√a = a 1/2
(√5) 12
when x is positive (√X) 12
(512) 1/2
56
when x is positive (X 12)1/2
x6
253/2
√253
numerator = power
denominator = root
Dividend = Quotient + Remainder
Divisor Divisor
Dividend = quotient x divisor + remainder
take a non square root
3√216
take the root and divide it into prime factors
216 = 3x3x3x2x2x2 =63
√2 ≈
√3 ≈
√5 ≈
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.5
Quadratic equation
ax2+bx+c = 0
-b ± √b2- 4ac
2a
to simplify a problem w/ a root in the demoninator…
multiple by the root
4 x √2 = 4√2 = 2√2
√2 x √2 2 .
to simplify a deonominator with a sum or difference of a root
multiply by the inverse
_4 _ x 2 + √2 = 4(3√2) = 12√2
3 - √2 x 3 + √2 (3 - √2)(3 + √2) 7
working with 2 absolute value equations
I x + 2 I < I 3x - 2 I
solve twice once with both having the same sign and once with one having a reversed sign
Adding or subtracting multiples of N the result is
If N is a divisor of X and Y then
a multiple of N
N is a divisor of X+Y
N is divisible by
the product of its primes
Primes of 72: 2, 2, 2, 3, 3
72 is also divisible by 4, 6, 8
ODD ± ODD =
EVEN ± EVEN =
EVEN
ODD ± EVEN =
ODD
When multiplying if any of the integers is even the results is?
EVEN
ODD divided by EVEN
Cannot be an integer
Sum of two primes
is even unless one of the primes is 2
Multiplying a group of numbers with an even number of negatives is ________
a group of numbers with an odd number of negatives is __________
Positive
Negative
All perfect squares
Have an odd number of total factors
because there is a pair.
The prime factorization of a perfect square contains…
The prime factorization of a perfect square contains only even powers of primes.
N! is a multiple of
N! is a multiple of all integers from 1 through N
To find the total number of factors
Find the prime factors and multiply the exponents
2000=24 x 53
there are 5 possible uses of 2 (0,1,2,3,4)
there are 4 possible uses of 5 (0,1,2,3)
4 x 5 = 20 there are 20 factors
Consecutive multiples of n have Greatest Common Factor of
n
weighted average
weight (data point) + weight (data point)…..
sum of the weight
= weighted average
standard deviation
small = clustered around mean
large = spread out
Variance = square of teh standard deviation
weighted averages with ratios
positive difference (x ratio) + negative difference (x ratio)
= 0
Quant Timing
60 min - 7 questions
45 min - 14 questions
30 min - 21 questions
15 min - 28 questions
