Number Sense

Question 1

Divisible by 3

Answer 1

Divisible by 3 is fhte sum of the digits is divisible by 3

Question 2

Divisible by 9

Answer 2

Divisible by 9 is fhte sum of the digits is divisible by 9

Question 3

Multiply a decimal with a big number

Answer 3

Trade decimal spaces 50,000 x .007 = 50 x 7

Question 4

When multiply or divide by a negative the answer is?

Answer 4

negative

Question 5

Prime

Answer 5

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

Question 6

Powers of 2

Answer 6

2¹=2; 2²=4; 2³=8; 2⁴=16; 2⁵=32; 2⁶=64; 2⁷=127; 2⁸=256; 2⁹=512; 2¹⁰=1024

Question 7

Powers of 3

Answer 7

3¹=3; 3²=9; 3³=27; 3⁴=81

Question 8

Powers of 4

Answer 8

4²=16; 4³=64

Question 9

Powers of 5

Answer 9

5²=25; 5³=125; 5⁴=625

Question 10

Square roots

Answer 10

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

Question 11

negative^ODD

Answer 11

Negative number

Question 12

negative^EVEN

Answer 12

Positive number

Question 13

Y^-3

Answer 13

Y^-3 = 1/y³

Question 14

A^b x A^c =

Answer 14

A^b x A^c = A^b+c

Question 15

X⁰ =

Answer 15

X⁰ = 1

Question 16

(X^a)^b =

Answer 16

(X^a)^b = X^ab

Question 17

a^b/ a^c =

Answer 17

a^b/ a^c = a ^b-c

Question 18

Cube Roots

3, 4, 5

Answer 18

3³ = 27; 4³ = 64; 5³ = 125

Question 19

Square Roots (bigger)

Answer 19

13² =169; 14²=196; 15²=225; 20² =400; 25²=625; 30² = 900

Question 20

a^-b =

Answer 20

a^-b = 1/a^b

Question 21

√ab =

Answer 21

√ab = √a x √b

Question 22

√a/b =

Answer 22

√a/b = √a / √b

Question 23

√a =

Answer 23

√a = a ^1/2

Question 24

(√5) ¹²

when x is positive (√X) ¹²

Answer 24

(5¹²) ^1/2

5⁶

when x is positive (X ¹²)^1/2

x⁶

Question 25

25^3/2

Answer 25

√25³ numerator = power denominator = root

Question 26

_Dividend_ = Quotient + _Remainder_ Divisor Divisor

Answer 26

Dividend = quotient x divisor + remainder

Question 27

take a non square root ³√216

Answer 27

take the root and divide it into prime factors 216 = 3x3x3x2x2x2 =6³

Question 28

√2 ≈ √3 ≈ √5 ≈

Answer 28

√2 ≈ 1.4 √3 ≈ 1.7 √5 ≈ 2.5

Question 29

Quadratic equation

Answer 29

ax²+bx+c = 0 _-b ± √b_²_ - 4ac_ 2a

Question 30

to simplify a problem w/ a root in the demoninator...

Answer 30

multiple by the root _4_ x _√2_ = _4√2_ = 2√2 √2 x √2 2 .

Question 31

to simplify a deonominator with a sum or difference of a root

Answer 31

multiply by the inverse _4 _ x _2 + √2_ = _4(3√2)_ = _12√2_ 3 - √2 x 3 + √2 (3 - √2)(3 + √2) 7

Question 32

working with 2 absolute value equations I x + 2 I \< I 3x - 2 I

Answer 32

solve twice once with both having the same sign and once with one having a reversed sign

Question 33

Adding or subtracting multiples of N the result is If N is a divisor of X and Y then

Answer 33

a multiple of N N is a divisor of X+Y

Question 34

N is divisible by

Answer 34

the product of its primes Primes of 72: 2, 2, 2, 3, 3 72 is also divisible by 4, 6, 8

Question 35

ODD ± ODD = EVEN ± EVEN =

Answer 35

EVEN

Question 36

ODD ± EVEN =

Answer 36

ODD

Question 37

When multiplying if any of the integers is even the results is?

Answer 37

EVEN

Question 38

ODD divided by EVEN

Answer 38

Cannot be an integer

Question 39

Sum of two primes

Answer 39

is even unless one of the primes is 2

Question 40

Multiplying a group of numbers with an even number of negatives is \_\_\_\_\_\_\_\_ a group of numbers with an odd number of negatives is \_\_\_\_\_\_\_\_\_\_

Answer 40

Positive Negative

Question 41

All perfect squares

Answer 41

Have an odd number of total factors because there is a pair.

Question 42

The prime factorization of a perfect square contains...

Answer 42

The prime factorization of a perfect square contains only even powers of primes.

Question 43

N! is a multiple of

Answer 43

N! is a multiple of all integers from 1 through N

Question 44

To find the total number of factors

Answer 44

**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**

Question 45

Consecutive multiples of n have Greatest Common Factor of

Answer 45

n

Question 46

weighted average

Answer 46

_weight (data point) + weight (data point)....._ sum of the weight = weighted average

Question 47

standard deviation

Answer 47

small = clustered around mean large = spread out Variance = square of teh standard deviation

Question 48

weighted averages with ratios

Answer 48

positive difference (x ratio) + negative difference (x ratio) = 0

Question 49

Quant Timing

Answer 49

60 min - 7 questions 45 min - 14 questions 30 min - 21 questions 15 min - 28 questions