GMAT MATH
How many multiples of 7 are there between 100 and 150?
(147 - 105)/7+1 = 7
(2 + 5)^3=
(7)^3 (NOT 2^3 + 5^3)
For an evenly spaced set, the mean and median of the set are equal to the average of the...
(First + Last) /2
The sum of consecutive integers =
(The Number of Items in the Set) X "Middle Number" Or Median
What is the units digit of 7^2*9^2*3^3?
To find the units digit of a product or a sum of integers, only pay attention to the units digit of the numbers you are working with. Drop any other digits.
When we divide the terms with the same base, we ___ the exponents.
subtract
Greatest Common Factor (GCF)
the largest divisor of two more integers
Least Common Multiple
the smallest multiple of two or more integers
x^3 < x^2. Describe the possible values of x.
x < 1 (except 0)
12 is divisible by 3 can be said in many different ways...
* 12 is a multiple of 3 * 12/3 is an integer *12 = 3n, where n is an integer *12 can be shared among 3 people so that each person has the same number of items *3 is a divisor of 12, or 3 is a factor of 12 *12/3 yields a remainder of 0 *3 "goes into" 12 evenly
Consecutive Multiples?
All the values in the set are multiples of the increment {12, 16, 20, 24}
Prime Factor?
Any number that is divisible by 1 and itself
If w, x, y and z are integers and w + x = y, is y divisble by z? (1) w and x have a remainder of 1 when divided by z (2) z = 2
C
If n is an integer and n^3 is between 1 and 100, inclusive, what is the value of n? (1) n = 2k + 1, where k is an integer (2) n is a prime number
C.
Is 28 divisible by 4?
Yes; because you can divide it by 2 twice. Or, when the last two digits are divisible by 4.
Is 72 divisible by 3?
Yes; the sum of its digits are 9, which is divisible by 3.
What is a multiple?
A multiple of an integer is formed by multiplying that integer by any integer, so 8, 16, 24 and 32 are some of the multiples of 8.
If the problem states or assumes that a number is an integer, you may need to use prime factorization to solve the problem.
* determining whether one number is divisible by another number * Determining the greatest common factor of two numbers * Reducing fractions * Finding the least common multiple of two (or more) numbers * Simplifying square roots * Determining the exponent on one side of an equation with integrer constraints
All evenly spaced sets are fully defined if the following are known...
*The smallest (first) or largest (last) number in the set *The increment (always 1 for consecutive integers) *The number of items in the set.
Fewer Factors, More Multiples.
...
For any set of consecutive integers with an EVEN number of items, the sum of all the integers is NEVER a multiple of the number of items.
...
For any set of consecutive integers with an ODD number of items, the sum of all the integers is ALWAYS a multiple of the number of items.
...
If you add or subtract two multiples N, you get another multiple of N
...
The product of k consecutive integers is always divisible by k!.
...
The sum of n consecutive integers id divisible by n if n is odd, but it is not divisible by n if n is even.
...
Two data sufficient statements always provide TRUE information
...
Yes/No data sufficiency problem, YES is a sufficient answer and NO is a sufficient answer. MAYBE is not a sufficient answer.
...
You can separate or combine the product or quotient of two roots
...
a^x + a^x + a^x = 3a^x
...
What are the first 10 prime factors?
2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
(216)^(1/3) = ...
216 = 3 x 3 x 3 x 2 x 2 x 2 = 6^3
a^x * b^x = (ab)^x
2^4 * 3^4 = 6^4
What number is 150% greater than 60?
60 (1 + 150/100) = 60*2.5 = 150
Is 27 a factor of 72?
72 Prime Factors = 2, 2, 2, 3, 3; 27 Prime Factors = 3, 3, 3. 72 has only two 3's and 27 has three 3's; therefore, 27 is not a factor of 72.
(2 x 5)^3 =
= (10)^3 = (2^3 + 5^3)
Sum of the number of consecutive integers =
= (Last - First + 1)
Sum of the number of consecutive multiples =
= (Last - First)/(Increment) + 1
If x is a positive integer, is x^3 - 3x^2 + 2x divisible by 4? (1) x = 4y + 4, y = integer (2) x = 2z + 2, z = integer
D. Both 1 and 2 are sufficient
Add or subtract 2 odd numbers, and the result is...
EVEN
Sum of any two primes above 2 is ...
EVEN
When you multiply integers, and any of the integers are even, the result is...
EVEN
Even +- Even =
Even
Odd X Even =
Even
Odd+- Odd =
Even
Even x Even =
Even (and divisible by 4)
Remainder 0
Even integers
What is a factor?
Factor is a positive integer that divides evenly into an integer (1,2,4 and 8 are all factors (also called divisors of 8).
Absolute Value?
How far away is the number from 0 on the number line?
Factor Foundation Rule
If a is a factor b, and b is a factor of c, then a is a factor of c. Or, any integer is divisible by all of its factors and it is also divisible by all all the factors of its factors.
What is the arithmetic mean (average) of a evenly spaced set?
The median or middle number (or average of middle number).
Add or subtract an odd with an even, and the result is...
ODD
Sum of 2 and any other prime is...
ODD
When you multiply integers, and none of the integers are even, the result is...
ODD
Odd +- Even =
Odd
Odd x Odd =
Odd
Remainder 1
Odd Integers (5/2 --> R = 1; 3/2 --> R =1)
If p is an integer, is p/18 an integer? (1) 5p/18 is an integer. (2) 6P/18 is an integer.
Rephrase to ask are there two 3's and and a 2 in the prime box of p?
Is 4,185 divisible by 9?
Yes; because the sum of the digits is divisible by 9 ((4+1+8+5 = 18)/9 = 2)
If x is an even integer, is x(x +1)(x+2) divisible by 4?
Yes. Setup prime boxes.
Is 456 divisible by 8?
Yes; because 456 is divisible by 2 three times. (456/2 = 228, 228/2 = 114; 114/2 = 57). Always check the last three digits of a larger number.
Is 48 divisible by 6?
Yes; because it is divisible by 2 (it ends with an 8, which is even) AND by 3 (4+8, which is divisble by 3).
When we multiply terms with the same base, we ___ the exponents.
add
For an evenly spaced set, the sum of the elements in the set equals
arithmetic mean (average) X the number of elements
x^a * x^b = x^(a+b)
c^3 * c^5 = c^8
All sets of consecutive integers are sets of...
consecutive multiples.
All sets of consecutive multiples are ...
evenly spaced sets.
To perform in a certain youth dance group, girls must be between 4 feet tall and 4 feet 6 inches, inclusive. If x represents a girl's height, in inches, write an absolute value equation for the heights of girls who are eligible to perform.
|x - 51| <= 3.
