1-Number Properties-Gmat

Front 1

When you see a GMAT question with the word "remainder" in it, chances are that you are being asked to apply __________________ rules?

Back 1

Divisibility Rules

Front 2

An integer is divisible by 2 if the integer is ____________?

Back 2

Even

Front 3

An integer is divisible by 3 if _________?

Back 3

Sum of the INTEGER'S digits is divisible by 3

Front 4

An integer is divisible by 4 if _________?

Back 4

Integer is divisble by 2 TWICE

Front 5

An integer is divisible by 5 if _________?

Back 5

Integer Ends in 0 or 5

Front 6

An integer is divisible by 6 if _________?

Back 6

Integer is divisible BOTH by 2 And 3

Front 7

An integer is divisible by 8 if _________?

Back 7

Integer is divisible by 2 THREE TIMES

Front 8

An integer is divisible by 9 if ____________?

Back 8

SUM of integer's digits is divisible by 9

Front 9

An integer is divisible by 10 if the integer ____________?

Back 9

ends in 0

Front 10

Factors are also called ____________

Back 10

Divisors

Front 11

A __________ of an integer is formed by multiplying that integery by any whole number

Back 11

Multiple

Front 12

A __________ divides evenly into an integer.

Back 12

Factor

Front 13

An integer is both a _________ and a ________ of itself.

Back 13

Factor and a multiple of itself

Front 14

Name the first 10 prime numbers

Back 14

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

Front 15

Mnemonic: _____ Factors and ______Multiples

Back 15

Fewer factors and More Multiples

Front 16

An integer that only has two factors, 1 and itself is a ______ number

Back 16

Prime Number

Front 17

Sum and Difference Rule

Back 17

If two numbers have a common divisor, their SUM and DIFFERENCE retain that divisor as well. EX: The sum of 64 and 40 is also divisible by 8. The difference between 64 and 40 is also divisible by 8.

Front 18

The #___ is NOT prime!!!

Back 18

1 IS NOT PRIME!!!

Front 19

If 72 is divisible by 12, then all the _______ of 12 are also factors of 72.

Back 19

Factors

Front 20

____________ can help solve problems about divisibility and GCFand LCM?

Back 20

Prime Boxes (Holds all prime factors of a number)

Front 21

How do you find the GCF of two numbers?

Back 21

Largest Number by which two integers can be divided. Find product of the common prime factors, using the lower power of the repeated factor.

Front 22

How do you find the LCM of two numbers?

Back 22

The smallest number that is a multiple of two integers. Find the product of ALL the prime factors of both numbers, using the higher power of the repeated factor.

Front 23

ODD AND EVEN POETRY: Addition and Subtraction

Back 23

Add 2 odds or add 2 evens, and EVEN you shall see. But add an odd with an even and oh how ODD t'will be.

Front 24

ODD AND EVEN POETRY: Multiplication

Back 24

Just one EVEN number in a multiplication set and an EVEN you will get.

Front 25

ODD AND EVEN POETRY: Division

Back 25

NO GUARANTEED OUTCOMES - b/c division of two integers may NOT necessarily lead an integer result.

Front 26

All prime numbers are _______ except for the number _____.

Back 26

All prime numbers are ODD, except the number 2.

Front 27

The sum of two primes is always _______ except when one of the primes is _____.

Back 27

EVEN except when one of the primes is TWO.

Front 28

The absolute value of any _________ number is always positive.

Back 28

non-zero

Front 29

If both extremes of a number set should be counted, then you need to _________!

Back 29

Add one before you are done!

Front 30

Sum of consecutive integers rule:

Back 30

1.) Find the middle of set 2.) Count the number of terms (inclusive) 3.) Multiply middle * number of terms. EX: What is the sum of all integers from 20 to 100 inclusive. 60 * 81 = 4,860

Front 31

Average term in a consecutive set:

Back 31

1.) If you know the FIRST and LAST terms of the set, simply find middle number 2.) If you only know the SUM of the set and the # OF TERMS in the set, use the average formula (sum of integers / # integers).

Front 32

The average of an odd number of terms will _____________

Back 32

Always be an integer

Front 33

The average of an even number of terms will ____________

Back 33

Never be an integer because there was no true middle number

Front 34

Special Products Rule: The product of any set of X consecutive integers is _________

Back 34

Divisible by X

Front 35

Special Sums Rule for a Set of Consecutive Integers with an odd # of terms => Find sum of 1 + 2 + 3 =>

Back 35

For any set of consecutive integers with an odd number of terms, the sum of all the integers is always a multiple of the # of terms. 6 is divisible by 3…

Front 36

What equation form might you use of any consecutive integers?

Back 36

n, n+1, n+2, n+3, n+4….

Front 37

If there is one even integer in a consecutive series, the product of the series is divisible by ___

Back 37

2

Front 38

If there are two even integers in a consecutive series, the product of the series is divisible by ___

Back 38

4

Front 39

If x^3 - 3 = p, and x is even, is p divisible by 4?

Back 39

NO => Factor x out of the expression => x(x2-1). Further factorization: x(x+1)(x-1). This is a product of consecutive integers. (x-1), x, (x+1). ODD, EVEN, ODD, so there are not two EVEN integers, just two ODD integers.

Front 40

The ___ exponent is dangerous: It hides the sign of the base!

Back 40

Even exponents hide the original sign of the base.

Front 41

When the base of an exponential expression is a fraction between 0 and 1, what occurs?

Back 41

When base is a fraction, then the value of the expression decreases…

Front 42

When you see a negative exponent, then it yields the _______ of the expression.

Back 42

Negative exponent => Reciprocal expression

Front 43

When multiplying exponential expressions with the same base, ____ the exponents first.

Back 43

ADD the exponents first

Front 44

When dividing expressions with the same base, _____ the exponents first.

Back 44

SUBTRACT the exponents first

Front 45

When multiplying expressions with the same exponent, ______ the BASES first

Back 45

MULTIPLY the BASES first

Front 46

When dividing expressions with the same exponent, _______ the BASES first

Back 46

DIVIDE the BASES first

Front 47

Can this expression be simplified? 7^4 + 7^6

Back 47

No, it can't be simplified…

Front 48

?? The radical (root) sign denotes only the non-negative root of a number. If √4 = x, what is x?

Back 48

2 I the only solution for X.

Front 49

You can never combine roots in _______ or _______. Only combine roots in ______ and _______.

Back 49

You can never combine roots in ADDITION and SUBTRACTION. You can only combine roots in MULTIPLICATION and DIVISION.

Front 50

ESTIMATE: √2 =

Back 50

1.4 or approx 3/2

Front 51

ESTIMATE: √3 =

Back 51

1.7

Front 52

ESTIMATE: √5 =

Back 52

2.2

Front 53

ESTIMATE: √6 =

Back 53

2.4

Front 54

ESTIMATE: √7 =

Back 54

2.6

Front 55

ESTIMATE: √8 =

Back 55

2.8

Front 56

2 ^ 3

Back 56

8

Front 57

3 ^ 3

Back 57

27

Front 58

4 ^ 3

Back 58

64

Front 59

5 ^ 3

Back 59

125

Front 60

In data sufficiency problems with ___________ - you can often rephrase the question to incorpoarate familiar rules.

Back 60

NUMBER PROPERTIES

Front 61

Translate Data Sufficiency: "If p is an integers, is (p/18) an integer?"

Back 61

1.) Is p divisible by 18? 2.) Is p divisible by 2, 3, 3?

Front 62

Always _______ algebraic expressions when you can to undisguise information in Data Sufficiency problems.

Back 62

Factor

Front 63

If x is a positive integer, is x^3 - 3x^2 + 2x divisible by 4?

Back 63

1.) Factor: x(x-2)(x-1). 2.) Recognize consecutive integers 3.) If x is even, then the consecutive integers are odd * even * odd = not divisible by 4. If x is odd, then the consecutive integers are even * odd * even = divisible by 4. REPRHASE: Is x even? OR Is x-1 a multiple of 4?

Front 64

Two data sufficiency statements always provide ______ information. Therefore:

Back 64

TRUE. Information in the two statements cannot contradict eachother.