GMAT lessons (arithmetic)

What is the sum of consecutive odd integers?

(2X-1) + (2X+1) = 4X. Must be a multiple of 4

The number of consecutive even or odd numbers is?

(L-F)/2 + 1 OR range/2 + 1

How to find number of distinct factors

(P+1)(q+1)(r+1) where p,q,r are the exponents of the prime factorization

What is a multiple of all integers

0

The first 10 non negative integers are

0,1,2,...8,9

How many solutions does a cube root have?

1

What is a factor of all integers?

1

Probability of an event not occuring

1 - probability that the event occurs

millions

1,000,000 or 10^6

The first 10 positive integers are

1,2,3...9,10

How to calculate variance

1. Subtract each score from the mean 2. Square every deviation of the mean 3. Add them all up 4. Divide by how many there is Take the square root of this to calculate standard deviation

√2

1.4

√3

1.7

hundredth digit

10^-2

millionths

10^-6

1/9 is what percent

11%

1/8 is what percent

12.5%

5^3

125

1/7 is what percent

14%

1/6

16 2/3%

13^2

169

14^2

196

How many solutions does a square root have?

2

The second 10 positive integers are?

2,3,4...10,11

√5

2.2

6^3

216

16^2

256

17^2

289

consecutive odd integers

2X-1, 2X+1

consecutive even integers

2X-2, 2X, 2X +2

18^2

324

7^3

343

19^2

361

8^3

512

25^2

625

4^3

64

9^3

729

Intersection (A and B)

A set of all elements that are both in Set A and Set B

prime number

A whole number that has exactly two factors, 1 and itself.

The ratio of males to females is 2 to 3. If the number of males is 10, what is the number of females?

A:B = C:D is equal to AD = BC. So 2:3 = 10:F —> 2F = 30. F =15

Or

Addition

Percent increase or decrease

After - before/ before times 100

If the range is zero

All elements have the same value, standard deviation is 0. Average = median

How to find the nth term of an arithmetic sequence

An = A1 + (n-1)d

How to find the nth term of a geometric sequence

An = A1*R^(n-1)

permutation

An arrangement of objects in which order is important Look for words such as "first" "second" or instanced where they need to pick a president and Vice President

Median

Another type of center for a list of numbers. Order the numbers in least to greatest and find the middle

Transforming fractions to decimals

Count the number or zeros. Example 15/10^7. This has 7 zeros. Write out 0.0000000 and then cross out the last 2 zeros and replace with 15. Answer is 0.0000015. Number of zeros equals the power of 10

The union of A and B (number of elements)

Elements in A + elements in B - the intersection of A and B

If one factor of a number is even then the number is

Even

mutually exclusive

Events that cannot occur at the same time Intersection of two events = 0. Think flipping of one coin, can either be heads or tails

Greatest number of prime factors of a number

Find the prime factorization and count how many unique numbers there are disregarding exponents.

Range

Greatest value - least value

What is the range of the first 10 consecutive even numbers.

L-F/2 + 1 = 10. Range/2 + 1 = 10 Range = 18

How to divide decimals

Make divisor into an integer

|x+y| is always ≤ |x| + |y|

Memorize this. Works with all numbers

Of

Multiply ( write X)

Process to divide fractions

Multiply by reciprocal or later number

If A<B is A^2<B^2

NO, in the case where A is negative and b is positive it's not always true. However if A<B<0 is true, then A^2<B^2 is true

Is 1 a prime number?

No, it does not have indistinct factors.

Standard deviation of 1,2,3 > standard deviation of 2,3,4?

No, parralel movement of data, when you add same amount to each element, does not affect standard deviation. Standard deviation is the separation of numbers. In the example all the elements are 1 away from eachother

Can you simplify AB = 1 to A= 1/B?

No, you cannot divide by variable in case it's equal to 0

geometric average

Nth root of the product. EX: geometric average of 2,9and 12 equal to cube root of (2X9X12) Geometric average a,b = root(ab)

irrational numbers

Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.

Is X < X^2< X^3

Only if X>1; if 0<X<1, the opposite is true

Is the percent increase/decrease equal to the percent change?

Only in the case of percent increase. For percent decrease, percent decrease has an opposite sign as percent change. EX: the percent change is -20%. The percent decrease is 20%

Probability of E or F

Probability of E + probability of F - probability of both e and f (intersection) Otherwise known as the union of e and f

Simplify A/BC = AC/B

Reduce by A/B (since it's on both sides of the equation). Left with 1/C = C. C must be 1

Union (A and B)

Set of all elements that are in either A or B

sum of a geometric sequence

Sn=a1(1-r^n)/1-r

arithmetic average

Sum of n divided by n. Also called mean Average of a,b = (a+b)/2

If the average and the least number are equal?

The average is equal to the median

units digit

The digit in the one's place. (For 287, the number 7is in the units or ONES place.)

absolute value

The distance a number is from zero on a number line

Harmonic Mean

The mean of n numbers expressed as the reciprocal of the arithmetic mean of the reciprocals of the numbers Harmonic average a,b = 2ab/a+b

Standard deviation

The more the data are spread from the mean the higher the standard deviation Square root of the variance

independent events

The outcome of one event does not affect the outcome of the second event Intersection of two events E and F = probability of e multiplied by probablilty of F Think flipping of two coins. One result does not affect the other

Mode

The value that occurs most frequently in a given data set.. note that the mode is not unique, there can be multiple in a data set

If XY<0 and X>Y

Then X HAS TO BE POSTIVE and Y has to be negative. The first part tells you they have opposite signs

Disjoint or mutually exclusive

Two sets that have no common elements

percent

Write 1/100

What is the sum of 2 consecutive integers (odd/even)

X + X+1 = 2X +1 Which must be odd

Remainder formula

X = QN + R Where X = dividend (# being divided) Q = quotient (number yielded when X divided by N) N = divisor (number being divided by) R = remainder

If A<B, is A+ 1< B+ 1?

Yes, you can add a constant to both sides without changing the direction

combination

a grouping of items in which order does not matter Selecting 2 reps Frkm 5 members = n(n-r+1)/r = 5(5-2+1)/2 = 5(4)/2 =10 Formula= (n)(n-1)(n-2)...(n-r+1)/r!

How do you multiply decimals?

count the number of decimal places in the factors because this will determine the number of places in the product. To multiply 1.05 by 5.25, multiply as you would whole numbers: 105⋅525=55125 Then count the number of places in both factors (there are four decimal places). Move four decimal places to the left in the result of 55125, and you get 5.5125, the correct answer.

Even times odd

even

even times even

even

odd + odd

even

A number is divisible by 8

if the number formed by the last three digits is divisible by 8

A number is divisible by 6 if

its divisible by 2 and by 3.

A number is divisible by 4 is...

its last two digits are divisible by 4.

Probability

likelihood that a particular event will occur. Number of cases that an event will occur over all possible events

even + odd =

odd

odd times odd

odd

Integers are

positive and negative whole numbers and zero

A number is divisible by 9 if

the sum of digits is divisible by 9.

A number is divisible by 3 if ...

the sum of its digits is divisible by 3.

Consecutive integers

x, x+1, x+2 BUT should use X-1,X,X+1 when solving problems

Remember this: √(a^2b) =

|a|√b