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GMAT > Number Properties > Flashcards

Number Properties Flashcards

1
Q

Properties of 0

A

Integer
Neither positive nor negative
Even
Not prime

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2
Q

Properties of 1

A

Integer
Positive
Odd
Not prime

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3
Q

Properties of 2

A

Integer
Positive
Even
Prime

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4
Q

When do you reverse the sign in an inequality?

A

When you multiply or divide by a negative number across the inequality
-(x/5) > 1
x < -5

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5
Q

Multiplying and dividing fractions

A

Multiply: simply multiply across

Divide: flip second fraction and multiply

Since fraction bar indicates division, same rule applies to fractions within fractions
3/4 ÷ 9/10 = 3/4 * 10/9 = 5/6

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6
Q

Reducing LARGE fractions

A

Break large fraction down into primes and then cancel

10/21 * 7/8 = (25)(7)/(37)(222) = 5/12

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7
Q

Adding or subtracting fractions with common denominator

A

Only add or subtract numerator

3/4 + 2/4 = 5/4
8/11 - 3/11 = 5/11

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8
Q

Adding and subtracting fractions with DIFFERENT denominators

A

Method 1: multiply each fraction by another fraction that makes both bases common. Then add or subtract

Method 2: bowtie (criss cross)
First multiply denominators to form base. The cross multiply numerators and denominators and add or subtract the products.
2/7 + 3/4 = (42) + (37) / 28 = 29/28

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9
Q

2/3 - 1/2 ÷ 1/12

A

(2/3 - 1/2) = 4-3/6 = 1/6
12(1/6) = 2
2

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10
Q

Order of operations

A

PEMDAS

Work exponents/roots as well as m,d,a,s from left to right

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11
Q

Factors

A

numbers that can be multiplied to make another number (x is a factor of y if y is divisible by x, where x and y are integers)

1,6,2,3 are the factors of 6 (factor pairs)

Prime factors - factor tree

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12
Q

A number is divisible by 2 if

A

it is even

ex. 110

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13
Q

A number is divisible by 3 if

A

its digits sum to multiple of 3

ex. 18255 (1+8+2+5+5 = 21)

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14
Q

A number is divisible by 4 if

A

Its last 2 digits are multiple of 4

Ex. 59456 (56÷4 = 14)

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15
Q

A number is divisible by 5 if

A

it ends in a 0 or 5

Ex. 65, 70

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16
Q

A number is divisible by 6 if

A

Its a multiple of both 2 and 3

Ex. 588 (even and sums to 18)

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17
Q

A number is divisible by 7

A

Take LAST digit and double it. Subtract answer from remaining digits - divisible by 7 if ends in 7

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18
Q

A number is divisible by 8 if

A

Its last 3 digits are multiple of 8

Ex. 17336 (336÷8 = 42)

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19
Q

A number is divisible by 9 if

A

its digits add up to a multiple of 3 and 9

Ex. 6417 (6+4+1+7 = 18)

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20
Q

A number is divisible by 10 if

A

it ends in a 0

Ex. 2,984,150

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21
Q

A number is divisible by 12 if

A

its a multiple of both 3 and 4

Ex. 4932 (32÷4 = 8; 4+9+3+2 = 18)

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22
Q

Multiples

A

numbers that can be made by multiplying by a certain number (all the numbers of an integer, y, where +/-1y, +/-2y…)

Multiples of 6: 6, 12, 18…

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23
Q

Least Common Multiple

A

the least common multiple of two integers is the smallest integer that is a multiple of both

to find LCM: break down multiples into prime factors and multiply largest common primes

ex. 18 = 2 x 3^2 and 24 = 2^3 x 3
LCM: 2^3 x 3^2 = 72

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24
Q

Exponent

A

exponents are just shorthand to express multiplication, and exponents can be negative (a number raised to a negative exponents is the reciprocal of that number raised to a positive exponent)

ex. x^-2 = 1/x^2

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25
Q

To multiply powers with the SAME base

A

add exponents

ex. 2^3 * 2^2 = 2^5

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26
Q

To divide powers with the SAME base

A

subtract exponents

ex. y^9/y^4 = y^5

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27
Q

When exponents have different bases, you CANNOT just add or subtract

A

exs.

x^4 * y^6 ≠ (xy)^10
x^5 + X^4 ≠ X^9

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28
Q

A negative number raised to an EVEN power becomes positive

A

exs.

(-4)^2 = 16
(-1/2) = 1/4
29
Q

A negative number raised to an ODD power remains negative

A

exs.

(-2)^3 = -8
(-1/3)^3 = -1/27
30
Q

When raising a power to power, MULTIPLY the exponents

A

exs.

(x^3)^5 = x^15
(3^2)^3 = 3^6 = 729
31
Q

When raising a product in PARENTHESES to a power, DISTRIBUTE the power over BOTH factors

A

exs.

(x^2*y^4)^3 = x^6*y^12
(2x^2)^4 = 2^4*x^8 = 16x^8
32
Q

Any number raised to the exponent 1

A

equals itself

exs.
2^1 = 2
-7^1 = -7

33
Q

1 raised to any exponent

A

equals 1

exs.
1^2 = 1
1^0 = 1

34
Q

0 raised to any power OTHER than 0

A

equals 0

exs.
0^4 = 0
0^1 = 0

35
Q

Any number raised to the 0

A

equals 1

exs.
3^0 = 1
(.34)^0 = 1
TT^0 = 1

36
Q

0 raised to the 0 power is

A

UNDEFINED

37
Q

Any positive number greater than 1 gets _____as it is raised to a higher power

A

LARGER

exs.
2^2 = 4
2^3 = 8
2^4 = 16

38
Q

Any positive number less than 1 (fractions) gets _____ as it is raised to a higher power

A

SMALLER

exs.
(1/3)^2 = 1/9
(1/3)^3 = 1/27

39
Q

Roots can also be expressed as factional exponents

A

exs.

√ x = x^1/2
4^1/2 = √4 = 2
^3√x = x^1/3
8^1/3 = ^3√8 = 2

40
Q

Square roots with SAME base can be added or subtracted

A

exs.

4√3 + 7√3 = 11√3
5√x - 2√x = 3√x
BUT
3√6 + 3√3 ≠ 3√9 (the numbers inside radicals are NOT the same)

41
Q

The product of square roots is EQUAL to the square root of the product

A

exs.

(√3)(√7) = √21
√721 = (√9)(√4)(√2) = 6√2
42
Q

The quotient of square roots is EQUAL to the square root of the quotients

A

exs.

√4/√2 = 2
√63/√7 = √9 = 3
43
Q

When taking the square root of a fraction, the result will always be _____ than the fraction itself

A

LARGER

ex.
√1/4 = 1/2
√1/4 > 1/4

44
Q

E x E

A

E

45
Q

E x O

A

E

46
Q

O x O

A

O

47
Q

E +/- E

A

E

48
Q

E +/- O

A

O

49
Q

O +/- O

A

E

50
Q

Prime numbers between 1 - 10

A

2, 3, 5, 7

51
Q

Prime numbers between 10 - 20

A

11, 13, 17, 19

52
Q

Prime numbers between 20 - 30

A

23, 29

53
Q

Prime numbers between 30 - 40

A

31, 37

54
Q

Prime numbers between 40 - 50

A

41, 43, 47

55
Q

Prime numbers between 50 - 60

A

53, 59

56
Q

Prime numbers between 60 - 70

A

61, 67

57
Q

Prime numbers between 70 - 80

A

71, 73, 79

58
Q

Prime numbers between 80 - 90

A

83, 89

59
Q

Prime numbers 90 - 100

A

97

60
Q

Absolute value

A

the distance between a number and o on the number line

61
Q

P x P

A

P

62
Q

N x N

A

P

63
Q

P x N

A

N

64
Q

Common radical approximations

A 
TT ≃ 3
√1 ≃ 1
√2 ≃ 1.4
√3 ≃ 1.7
√4 = 2
65
Q

Radical rules

A

√a√b = √ab
√a/√b = √a/b
a√c + b√c = (a + b)√c
(√a)^2 = a

BUT
√a + √b ≠ √a+b
√a - √b ≠ √a-b

66
Q

Exponent rules

A 
x * x = x^2 
x^-a = 1/x^a
x^0 = 1
x^a*x^b = x^a+b
(x^a)^b = x^ab
x^a/x^b = x^a-b
(negative)^odd = negative
(negative)^even = positive
67
Q

Greatest common factor

A

largest factor that 2 numbers have in common

GCF: find prime factors of both integers and combine common ones
ex. 36 (2^23^2) and 54 (23^3) both have 2 and 3^2 in common so 233 = 18 = GCF

68
Q

Comparing fractions

A

need common denominator but if more than 2 fractions, compare 2 at a time

use bowtie (criss-cross) method to see which is larger

GMAT (12 decks)

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