Cliffs Notes: Gre Prep: Part 1: Arithmetic

Front 1

Define: Natural Numbers

Back 1

1,2,3,4

These are called natural or counting numbers.

Front 2

Define: Integers

Back 2

-2,-1,0,1,2

These are called Integers.

Front 3

Define: Rational Numbers

Back 3

3/2, 7/8

The decimal is ends.

Front 4

Is 5 a rational number?

Back 4

Yes!

Remember 5 can always be written 5/1. So yes.

Front 5

Define: Irrational Number

Back 5

sqrt 3 or pi

The decimal never ends!

Front 6

Real numbers consist of all rational and irrational numbers.

(True/False)?

Back 6

True!

Front 7

Define: Prime Number

Back 7

A prime numberis a number that can be evenly divided by only itself and 1.

e.g: 19

Front 8

What is the ONLY...repeat ONLY even prime number?

Back 8

2

Front 9

Are Zero and 1 prime numbers?

Back 9

NO!

Front 10

What is the opposite of prime numbers?

Back 10

Composite numbers

A composite number is a number divisible by more than just 1 and itself: 4,6,8...

Front 11

Define: Commutative

Back 11

Means that the order does not make any difference.

2+3=3+2

Front 12

Is subtraction commutative?

Back 12

No!

Front 13

Define: Associative

Back 13

Associative means that the grouping does not make any difference.

(2+3) +4 = (4+3) + 2

Front 14

Does Associative property hold for subtraction?

Back 14

No!

Front 15

Any number plus its additive inverse is equal to what?

Back 15

Zero

Front 16

3+0=3

This is an example of what?

Back 16

Identity Element

Front 17

When you multiply two odd numbers, the answer is always an odd number.

(True/False)

Back 17

True

This is an example of closure. Because you start with two odd numbers and the result is two odd numbers.

Front 18

What is the identity element for multiplication?

Back 18

1

Front 19

1. The multiplicative inverse for a number will always be?

2. A number multiplied by its multiplicative inverse will be?

Back 19

The reciprocal of the number.

The answer will always be 1.

Front 20

The multiplicative inverse of "a" is what?

Back 20

1/a

Front 21

2 (3+4) = 2(3) + 2(4)

This is an example of what property?

Back 21

The distributive property.

Front 22

Write 300+40+5 in expanded notation.

Back 22

(3*100)+(4*10)+(3*1)

This is used to find out the place value (10ths position..etc.) of each digit.

Front 23

4^0 = ?

Back 23

1

Any digit to the zero power is equal to 1.

Front 24

Write: 3.581 in expanded notation.

Back 24

(3*10^0)+(5*10^-1)+(8*10-2)+(1*10^-3)

Front 25

-3 > -2

(True/False)

Back 25

False!

Whatever lies left on the number line is the larger number!

Front 26

0/5
5/0

Which one is undefined?

Back 26

5/0

0/5 is just zero! 5/0 is undefined.

Front 27

Define: Proper Fraction

Back 27

This simply means the denominator is larger than the numerator.

Front 28

Define: Improper Fraction

Back 28

The numerator is larger than the denominator.

8/3

Front 29

What are the factors of 8?

Back 29

1,2,4,8

Because 1*8=8 and 2*4=8, so 1,2,4,8 are factors.

Front 30

What are the multiples of 5?

Back 30

5,10,15,20,25,30,35,40...etc.

Front 31

What are the first three common multiples of 2 and 3?

Back 31

6,12,18

Front 32

Quickly change .062 into a fraction!

Back 32

62/1000 or simplified 31/500

Remember that .062 its last number place is the thousandth so just divide by 1000.

Front 33

Change 35,000 into scientific notation.

Back 33

3.5*10^4

notice that if you multiply it it should equal your original number.

Front 34

Change .00047 into scientific notation.

Back 34

4.7*10^-4

notice that if you mutliply it, it should equal the same number.

Front 35

What is 4^1?

Back 35

4

Any number raised to the 1 is equal to itself.

Front 36

3^3*3^4= ?

Back 36

3^7

remember if you are multiplying variables with same bases, you just add the exponents.

Front 37

-sqrt9 = ?

Back 37

This is equal to -3

If a negative sign is in front of the square root, the answer must be negative as well.

Front 38

What is the probability that on two consecutive rolls of a die the numbers will be 2 and then 3?

Back 38

1/36

Since the probability of getting a 2 on the first roll is (1/6) and the probability of getting a 3 on the second roll is (!/6) and since the rolls are INDEPENDENT of each other, simply multiply these two answers.

Front 39

What is the probability of tossing heads three times in a row with a coin?

Back 39

1/8

Since each toss is INDEPENDENT and the odds are 1/2 for each toss 1/2*1/2*1/2= 1/8

Don't you dare multiply 1/2*3

Front 40

What is the probability of rolling two dice in one toss so that they total 5?

Back 40

1/9

Since there are six possible outcomes on each die, the total possible outcomes for two dice is 6*6=36. The favorable outcomes are (1+4),(4+1),(2+3),(3+2). Thus there are four favorable outcomes. 4/36=1/9

Front 41

Probability=

Back 41

# of favorable outcomes/# of possible outcomes

Front 42

Define: Combination

Back 42

THE TOTAL NUMBER OF INDEPENDENT CHOICES

If there are a number of sucessive choices are independent of each other (order makes no difference), the total number of possible choices is a combination.

Front 43

Define: Permutation

Back 43

THE TOTAL NUMBER OF DEPENDENT CHOICES

If there are a number of successive choices to make and the choices are affected by the previous choice or choices (dependent upon order), then permutations are involved.

Front 44

How many possible combinations of shirts and ties are there if there are five different color shirts and three different color ties?

Back 44

5 * 3= 15

This is the definition of a combination. The choices are independent of the last chosen. So you just multiple the nubmers together. In addition, notice that the question itself ask for the combination.

Front 45

4!

This is read like what? and what is the answer?

Back 45

factorial 4 or 4 factorial.

The answer is 4*3*2*1=24
This is a permutation

Front 46

How many different ways can you arrange the letters STOP?

Back 46

4! or 24

Here the first letter you choose you have 4 possible outcomes, not the 2nd action is dependent of on the first because now the second letter you choose there are only 3 possible letters, so on and so forth. This is a permutation. So the answer is 4*3*2*1=24

Front 47

C(n,r)

This is read how?

Back 47

The number of combinations of "n" things taken "r" at a time.

Front 48

What is the equation for C(n,r)?

Back 48

n!/r!(n-r)!

Front 49

If, from among five people, three executives are to be selected, how many possible combinations of executives are there?

Back 49

10

Read this problem again and realize that this is a combination of a combination question and a permutation question. Because you are looking for different combinations of 3 but there are more than 3 people to choose from. So it is not inclusive. Also it is a permutation at the same time because your first choice affects your second. So now establish your n and r. n=5 or total number of people and r=3, the number to be taken at a time.

The result is 5!/(3!*2!)

Front 50

P(n,r)

Back 50

The number of permutations of "n" things taken "r" at a time.

Front 51

If, from among five people, three executives are to be selected, how many possible permutations of executives are there?

Back 51

!5/(5-3)!=60

Notice that there are 10 combations, but here we want to know the order in which they lie. So effectively each combination can be arranged in 6 different ways. You can verify this by noticing that there are 3 per group. So there are 3! cominbation per group or 6. There are 10 possible combination with 6 possible order or permutations per combination resulting in the answer of 60!

Front 52

Define: Mode

Back 52

The number appearing most frequently in a group.

Front 53

What is the weighted mean of three test averaging 70% and seven test averaging 85%?

Back 53

80.5%

Remember the WACC in finance. Weighted mean is simply the weighted average. So 70(3/10)+85(7/10)=80.5%

Front 54

Define: Range

Back 54

The range is the difference between the largest and the smallest number.

Front 55

What is the range of 3,5,7,3,2?

Back 55

5

7-2=5. The range is not 2 to 7. Although that is what the numbers range from.

Front 56

"Measures of Central Tendencies" are problems that simply deal with?

Back 56

Averages, means, modes, ranges...etc.

Front 57

You are trying to find the median and you have an even amount of number, what do you do?

Back 57

You take the two middle numbers and you average them together, that is your median.

Front 58

What are the three steps in finding patterns in a number series?

Back 58

1. Write the difference in numbers on top of the numbers.
2. If no pattern is obsered, then see if the numbers are being added, subtracted, multiplied or divided (the 4 operatiosn, remember that subtraction & division are rarer).
3. Finally observe every other (or even every third!) number to observe a pattern. Remember that the operatiosn could differ.