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

Divisibility Rules


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

Even


An integer is divisible by 3 if _________?

Sum of the INTEGER'S digits is divisible by 3


An integer is divisible by 4 if _________?

Integer is divisble by 2 TWICE


An integer is divisible by 5 if _________?

Integer Ends in 0 or 5


An integer is divisible by 6 if _________?

Integer is divisible BOTH by 2 And 3


An integer is divisible by 8 if _________?

Integer is divisible by 2 THREE TIMES


An integer is divisible by 9 if ____________?

SUM of integer's digits is divisible by 9


An integer is divisible by 10 if the integer ____________?

ends in 0


Factors are also called ____________

Divisors


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

Multiple


A __________ divides evenly into an integer.

Factor


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

Factor and a multiple of itself


Name the first 10 prime numbers

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


Mnemonic: _____ Factors and ______Multiples

Fewer factors and More Multiples


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

Prime Number


Sum and Difference Rule

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.


The #___ is NOT prime!!!

1 IS NOT PRIME!!!


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

Factors


____________ can help solve problems about divisibility and GCFand LCM?

Prime Boxes (Holds all prime factors of a number)


How do you find the GCF of two numbers?

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


How do you find the LCM of two numbers?

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.


ODD AND EVEN POETRY: Addition and Subtraction

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.


ODD AND EVEN POETRY: Multiplication

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


ODD AND EVEN POETRY: Division

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


All prime numbers are _______ except for the number _____.

All prime numbers are ODD, except the number 2.


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

EVEN except when one of the primes is TWO.


The absolute value of any _________ number is always positive.

nonzero


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

Add one before you are done!


Sum of consecutive integers rule:

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


Average term in a consecutive set:

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).


The average of an odd number of terms will _____________

Always be an integer


The average of an even number of terms will ____________

Never be an integer because there was no true middle number


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

Divisible by X


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

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…


What equation form might you use of any consecutive integers?

n, n+1, n+2, n+3, n+4….


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

2


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

4


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

NO => Factor x out of the expression => x(x21). Further factorization: x(x+1)(x1). This is a product of consecutive integers. (x1), x, (x+1). ODD, EVEN, ODD, so there are not two EVEN integers, just two ODD integers.


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

Even exponents hide the original sign of the base.


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

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


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

Negative exponent => Reciprocal expression


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

ADD the exponents first


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

SUBTRACT the exponents first


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

MULTIPLY the BASES first


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

DIVIDE the BASES first


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

No, it can't be simplified…


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

2 I the only solution for X.


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

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


ESTIMATE: √2 =

1.4 or approx 3/2


ESTIMATE: √3 =

1.7


ESTIMATE: √5 =

2.2


ESTIMATE: √6 =

2.4


ESTIMATE: √7 =

2.6


ESTIMATE: √8 =

2.8


2 ^ 3

8


3 ^ 3

27


4 ^ 3

64


5 ^ 3

125


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

NUMBER PROPERTIES


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

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


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

Factor


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

1.) Factor: x(x2)(x1). 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 x1 a multiple of 4?


Two data sufficiency statements always provide ______ information. Therefore:

TRUE. Information in the two statements cannot contradict eachother.
