GRE Flashcards

Question

T or F: When adding or subtracting decimal #'s, you want to line up the decimals and fill in the blanks with zeros?

Answer 1

True Always line up the decimals when adding or subtracting

Answer 2

False. Always line up the decimals when adding or subtracting numbers

Answer 3

False. When multiplying decimals, complete the multiplication like normal, then count the total 3 of decimal places to the right of the decimal, and finally, move the decimal that many places to the left. .15 x .01 = .0015 (Notice 4 decimal places)

Answer 4

Dividend is to the left the sign and the divisor is to the right 10 = dividend, 5 = divisor 3 = dividend, 7 = divisor 1.2 = dividend, 4 = divisor

Answer 5

56/10000 Note: 1. Remove the decimal and place that number in the denominator 2. Count the number of decimal places and add that many zero's to 1

Answer 6

Rule: If X is between 0 and 1 (Positive, proper fraction), then X²\< X \< SQRT(x)

Answer 7

With all positive #'s, including positive fractions, the largest number, when squared, will still be the biggest.

Answer 8

Answer: about 254,000 3²= 9 500 x 500 = 250,000, but it's a little bit less.

Answer 9

51 Note: Must use PEMDAS. Multiply first, then add

Answer 10

87 ( 44 + 56) = 87 ( 100) = 8700

Answer 11

_5 ( 1 + 2 + 3 + 4....)_ 6 ( 1 + 2 + 3 + 4....) numerator cancels w/ denominator leaving 5/6

Answer 12

5 (1.000001) / 9 (1.000001) = 5/9

Answer 13

1000 - 1 + 578 = 1578 - 1 = 1577

Answer 14

X \> X^2 Rule if X is proper fraction: X^2 \< X \< SQRTX X = 1/4 1/16 \< 1/4 \< 1/2

Answer 15

Less than Rule: X^2 \< X \< SQRT(x)

Answer 16

0,1,2,3,4,5,6,7,8,9 Note: Don't forget zero, dummy.

Answer 17

Ex: 100+101+102+103+104+106+107+108+109+110 N=11 11/2 (100+110) =

Answer 18

With consecutive #'s, the average of the set is also the median. Average = 104

Answer 19

The opposits is 2 The opposite of a number, is the number with the opposite sign. 2 = -2 1/4 = -1/4 -14 = 14

Answer 20

If Y = 1 or -1 **Dont forget -1**

Answer 21

Terminating or repeating decimals

Answer 22

Factors of ONLY 5 or 2

Answer 23

0! + 0! = 2! 1! + 0! = 2! 1! + 1! = 2!

Answer 24

Most negative When wanting to know the smallest fraction between -5/6 and -6/7, take the most positive fraction and that will also be the most negative.

Answer 25

-1 x -1 = 1 Note: Only two ways the product of two integers can equal 1

Answer 26

Zero! 1231231 x 0 = 0

Answer 27

Use whatever's in the denominator as a starting point to help factor.

Answer 28

(X+Y)²= X²+Y²+2xy = (x+y)(x+y)

Answer 29

(X - Y)² = (X - Y) (X - Y) = X² + Y²- 2XY

Answer 30

(X + Y) (X - Y) = X² - Y²

Answer 31

(X - 1) (X + 1)

Answer 32

(X - 3) (X + 3)

Answer 33

(2x - 10) (2x + 10)

Answer 34

(xy - 4) (xy + 4)

Answer 35

(1/6x - 5) (1/6x + 5)

Answer 36

(3¹⁵)² - (2¹⁵)² = (3¹⁵ - 2¹⁵) (3¹⁵ + 2¹⁵)

Answer 37

(2⁶ - 1) (2⁶ + 1) = 63 \* 65

Answer 38

(x⁵⁰)² - (y⁵⁰)² = (x⁵⁰- y⁵⁰) (x⁵⁰ + y⁵⁰)

Answer 39

(5! - 4!) (5! + 4!) = (120 - 24) (120 + 24) = 96 \* 144

Answer 40

= -1 This is another way to express -1. Be on the lookout.

Answer 41

x = 2, y = 4 is the only time 2⁴ = 4² ^{16 = 16}

Answer 42

You can only factor by grouping if: a/b = c/d

Answer 43

= (x-2) (x² - 3)

Answer 44

(x+4) (2x² - 1)

Answer 45

x = 0 x = -100 IF YOU DIVIDE OUT THE X BY ZERO, YOU WILL MISS THE POSSIBLITY THAT x = 0

Answer 46

x = -.12, .04 (x - 4/100) (x+ 12/100)

Answer 47

(x⁵⁰)² - (y⁵⁰)² / x⁵⁰ - y⁵⁰= (x⁵⁰ - y⁵⁰) (x⁵⁰ + y⁵⁰) / x⁵⁰ - y⁵⁰ = x⁵⁰ + y⁵⁰

Answer 48

1. Set each binomial equal to zero x+2 = 0 6 + 3/x = 0 2. Solve each for x

Answer 49

(1-x) (1+x)

Answer 50

10, 12, and 30

Answer 51

Dividend = Numerator Divisor = Denominator

Answer 52

Dividend = Numerator Divisor = Denominator

Answer 53

Zero Due to 5 x 2 pairs

Answer 54

N! 34 x 35 x 36 x 37 x 38 is divisible 5! ( = an integer) 1 x 2 x 3 x 4 is divisible 4! (= an integer)

Answer 55

2, 3, 7, or 8

Answer 56

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Answer 57

Yes, the prime factorization of a perfect sqaure will only contain even exponents.

Answer 58

0, 1, 8, 27, 64, 125, 216, 343, 512

Answer 59

The prime factorization of the denominator contains only 2's or 5's or both.

Answer 60

2, 3, 7, or 8

Answer 61

| X | Absolute value of x

Answer 62

X = |2| The value of any variable raised to an even exponent will never have a unique value (could be pos./neg.)

Answer 63

X^4 = 10000 10 x 10 x 10 x 10 = 10,000 X = |4| The value of any variable raised to an even exponent will never have one unique value (could be pos./neg.). \*\*The even exponent masks the sign\*\*

Answer 64

Rule 1: |a-b| ≥ |a| - |b| Rule 2: If b ≠ 0, and |a+b| = |a| + |b|, then 'a' and 'b' have the same sign and |a| ≥ |b|

Answer 65

total cost / total # of items = price per item

Answer 66

X (1 + y/100)

Answer 67

= x (1 + 50/100) = x (1 + 1/2) = x (3/2) = 3x/2

Answer 68

Profit = Total revenue - Total cost

Answer 69

(1/6) X + 55 = Y

Answer 70

1) x + y = 12 2) x = 1.5y

Answer 71

_M + 7 = 5_ H + 3 = 3

Answer 72

Distance = Rate x Time

Answer 73

Time = Distance/Rate

Answer 74

Rate = Distance/Time

Answer 75

Time = Change in D/ Change in Time

Answer 76

Add rate₁ and rate₂

Answer 77

Work_{object 1} + Work_{object 2} = Work_Total Find work of both respective objects and set equal to one

Answer 78

We know that either m or n is 0, or they have the same signs

Answer 79

Go take Module 9-12 Review Test

Answer 80

Go take Review Quiz #9

Answer 81

2. 5 x 10¹³ 1. As the number in front of the 'X' increases, the power of 10 decreases. 2. As the # in front of the 'X' decreases, the power of 10 increases

Answer 82

2. 5 x 10¹³ 1. As the number in front of the 'X' increases, the power of 10 decreases. 2. As the # in front of the 'X' decreases, the power of 10 increases

Answer 83

y = k/x or yx = k

Answer 84

Final/New Value = Initial Value \* [1 - ("% less than"/100)]

Answer 85

This means, "2 is what percent of .5"?

Answer 86

This means, ".5 is what percent of 2"?

Answer 87

Solution = (1.4)⁵ \* 100,000 Notes - "5" is the number of years 4^{any odd #} = a units digit ending in 4

Answer 88

#(A or B) = #A + #B - (Both A and B)

Answer 89

Sum of all items/ # of items

Answer 90

of terms \* average

Answer 91

100 - 50 + 1 = 51 When counting consecutive integers in a set that includes the first and last numbers (Inclusive), calculate by using: Highest # - Lowest # + 1 = Total

Answer 92

(39-18/3) + 1 = 8

Answer 93

50 - 10 = 40 people High # - Low # = Total

Answer 94

(500 + 100) / 2 = 300 ( H + L ) / 2 = Avg \*Can only be used with evenly spaced #'s\*

Answer 95

Highest # + Lowest number / 2

Answer 96

Sum = Avg \* Total #'s in set Avg = H + L / 2 Total # = Consecutive Int Formulas

Answer 97

WA = Sum of weighted terms (a \* x) + (b \* y) / Total number of weighted terms ( a + b)

Answer 98

Position of median = (N + 1) / 2 N = Total # of terms

Answer 99

**avg = (4 + 100)/ 2 = 52** ## Footnote 1. In this case the highest and lowest multiple's of 4 are 4 and 100. 2. Add the highest and lowest multiple's of 4 that fit within the parameters of 1- 100). 3. Divide the sum of these two ints. By two to get the average of the whole set.

Answer 100

nCk = n! / k! (n-k)! N = total objects K = # of objects selected

Answer 101

21/3¹ = 21/3 = 7 21/3² = 21/9 = 2 + remainder 7+2 = 9 3's \*\*must make sure that the denominator is prime factored\*\*

Answer 102

N consecutive integers must de divisible by N! 4 consecutive integers must be divisible by 4! 4 x 3 x 2 x 1 = 24

Answer 103

A fraction will terminate when the denominator of the reduced fraction contains only 2's, 5's, or both 2's and 5's and nothing else.

Answer 104

When dividing by 5, the remainder will always be the units over 5. 7/5 = Q r2