Math Concepts to Memorize

Question 1

Multiply Units - 10” long * 4” w * 7” h = ?

Answer 1

280 in³ (cubed)

Question 2

Distance/Work Rate Formula

Answer 2

Rate * Time = Distance/Work or Rate = Work/Time

Question 3

If an object moves the same distance twice at different speeds, the average will be…

Answer 3

closer to the slower speed. Pick a smart number for the distance and create a R*T=D chart for both trips. Trip 1: 4*3 = 12 Trip 2: 6*2 = 12 Aveg: ?*(3+2) = 24 ?*5=24 ?=4.8MPH

Question 4

When two machines work together ____ the rates

Answer 4

ADD the rates. Rate A + Rate B = Rate A+B

Question 5

2 Average Formals

Answer 5

Average = Sum/# of Terms OR Average * # of items = sum

Question 6

Small Standard Deviation =

Answer 6

Closely clustered data

Question 7

3 Properties of Evenly Spaced Sets

Answer 7

Arithmetic Mean = Median

Mean & Median = Avg of 1st & Last Terms

Sum of Elements = Mean * # of items

Question 8

Formula for Counting Integers in a Set

Answer 8

Last-First + 1 OR (Last-First) / Increment + 1

Question 9

5 Properties of Consecutive Integer Sets

Answer 9

Average First & Last Term to Find Middle

Count * of Terms (First-Last) + 1

Multiple middle term by # of terms

The average of an odd # of integers is an integer

The average of an even # of consecutive integers will never be an integer

Question 10

To Examine Overlapping Sets

Answer 10

Create a Double Set Matrix. Use algebra.

Question 11

To Examine 3 Overlapping Sets

Answer 11

Create A Venn Diagram. Work from Inside to Out.

Question 12

Solving Inequalities (mult/div & add/sub)

Answer 12

When you multiply or divide by a NEGATIVE, flip the sign. You can ADD inequalities when symbols face the same way. You can NOT SUBTRACT inequalities.

Question 13

If someone is younger ____ the difference to keep the parties equal.

Answer 13

ADD

Question 14

Formula for distance when traveling towards each other

Answer 14

Sum of Rates * Time to Meet = Initial Separation

Question 15

Formula for two parties working at different speeds, working together.

Answer 15

Add rates. 1/5 + 1/7 = 7/35 + 5/35 = 12/35

Question 16

Formula for speed as two people walk towards each other at different speeds.

Answer 16

Person 1 Rate + Person 2 Rate = Rate of Travel. i.e. 5MPH + 6MPH = 11MPH

Question 17

Setup for two different people walk towards each other but one starts 2 hours later.

Answer 17

R * T = D chart. One party will be T+2 (if time is in hours already).

Question 18

If one party is undoing the work of the other party _____ the rates of work.

Answer 18

SUBTRACT

Question 19

When comparing rates of work for different machines, first

Answer 19

express the rates in equivalent units. How much can it finish per second/minute/hour.

Question 20

x*x

Answer 20

x²

Question 21

square root 2 * square root 2

Answer 21

2

Question 22

pull out the common factor: x²y-xy² =

Answer 22

xy(x-y)

Question 23

14-3(4-6) =

Answer 23

20

Question 24

-(5²)=

Answer 24

-25

Question 25

3 x 99 - 2 x 99 - 1 x 99 =

Answer 25

0

Question 26

(2xy)²=

Answer 26

4x²y²

Question 27

3y + xy - 2y =

Answer 27

3y-2y+xy (3-2)y + xy 1y + xy (1+x)y (x+1)y

Question 28

12xy - (6x + 2y) =

Answer 28

12xy - 6x - 2y

Question 29

2x² - 4x² - 1x^{2 =}

Answer 29

(2-4-1)x² (-3)x² -3x²

Question 30

square root 3(sq root 2 + sq root 3) =

Answer 30

square 3 \* square 2 + square 3 \* square 3 square 6 + 3

Question 31

an integer is divisible by 3 if...

Answer 31

...the sume of the integer's digits is a multiple of 3.

Question 32

an integer is divisible by 9 if..

Answer 32

the sum of the integer's digits is a multiple of 9.

Question 33

All the primes less than 20 are...

Answer 33

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

Question 34

What is the factor foundation rule?

Answer 34

Every number is divisible by the factors of its factors. Also you can multiply two factors and it will still be divisble. (If 20 is divisible by 2 & 5, it is also divisible by 2 x 5).

Question 35

To find all the factors of a number...

Answer 35

setup a factors pairs table 1 x 30 2 x 15 3 x 10 5 x 6

Question 36

To find all the prime factors of a number...

Answer 36

use a factors tree. 28 2 \* 14 2 \* 7

Question 37

X is divisible by 10 & 17. Is X divisible by 5? Is X divisible by 170? Is X divisible by 15?

Answer 37

Yes (5 is a factor of 10) Yes (170 is the LCM of 10 \* 17) Maybe (5 is a factor but we don't know if a 3 is present)

Question 38

What does LCM stand for? What is the LCM of 6 & 9?

Answer 38

Least Common Multiple 18

Question 39

If x is divisible by A & by B then x is divisible by...

Answer 39

the LCM of A and B.

Question 40

When you combine two factors trees of x that contain overlapping primes...

Answer 40

drop the overlap.

Question 41

If x is divisible by 8, 12, and 45, what is the largest number that x must be divisible by?

Answer 41

Create factor trees for each number. Count the number of unique prime factors. *8 has three 2s so include * 2 x 2 x 2 *45 has two 3s and one 5* 3 x 3 x 5 *12 has two 2s and one 3 (but those are covered by previous factors)* add nothing 2 x 2 x 2 x 3 x 3 x 5 = 360

Question 42

7 x 6 =

Answer 42

42

Question 43

7 x 7 =

Answer 43

49

Question 44

8 x 7 =

Answer 44

56

Question 45

8 x 8 =

Answer 45

64

Question 46

4²=

Answer 46

16

Question 47

5²=

Answer 47

25

Question 48

6²=

Answer 48

36

Question 49

7²=

Answer 49

49

Question 50

8²=

Answer 50

64

Question 51

9²=

Answer 51

81

Question 52

11²=

Answer 52

121

Question 53

12²=

Answer 53

144

Question 54

13²=

Answer 54

169

Question 55

14²=

Answer 55

196

Question 56

15²=

Answer 56

225

Question 57

20²=

Answer 57

400

Question 58

30²=

Answer 58

900

Question 59

3³=

Answer 59

27

Question 60

3⁴=

Answer 60

81

Question 61

5³=

Answer 61

125

Question 62

2³=

Answer 62

8

Question 63

3³=

Answer 63

27

Question 64

4³=

Answer 64

64

Question 65

5³=

Answer 65

125

Question 66

10³=

Answer 66

1,000

Question 67

2³=

Answer 67

8

Question 68

2⁴=

Answer 68

16

Question 69

2⁵=

Answer 69

32

Question 70

2⁶=

Answer 70

64

Question 71

2⁷=

Answer 71

128

Question 72

2⁸=

Answer 72

256

Question 73

2⁹=

Answer 73

512

Question 74

2¹⁰=

Answer 74

1024

Question 75

4³=

Answer 75

64

Question 76

x² = 16 x equals ???

Answer 76

4 or -4

Question 77

Which is larger? (-3²) or (-3)²

Answer 77

(-3)² = 9 (-3²) = 3 x 3 x -1 = -9

Question 78

To multiply exponential terms with the same base ... y(y⁶) =

Answer 78

add the exponents. y¹ x y⁶ = y⁷

Question 79

When you divide exponential terms that have the same base, ... a⁵ / a³ =

Answer 79

subtract the exponents. a^5-3=a²

Question 80

For any nonezero value of a, a⁰=

Answer 80

1

Question 81

2^-3= *three forms of the answer*

Answer 81

2^-3 = 1/2³ = 1/8 = 0.125 ## Footnote

Question 82

When you move an exponent from the top to the bottom of a fraction (or vice versa)... _ 1 _ z^-4

Answer 82

Switch the sign of the exponent. If you move the entire denominator, leave 1 behind. _ 1_ = _1\*z_⁴ = _z_⁴ z^-4 = 1 = 1

Question 83

When you raise something that already has an exponent to another power... (a²)⁴=

Answer 83

multiply the exponents together. (a²)⁴= a^2*4 = a⁸

Question 84

When multiplying exponents with different bases.... 2² x 4³ x 16=

Answer 84

try breaking down the bases into prime factors. 2² x 4³ x 16 = 2² x (2²)³ x 2⁴ 2² x 2⁶ x 2^{4 =} 2²⁺⁶⁺⁴ 2¹²

Question 85

When you apply an exponent to a product... (xy)³ = (wz³)^x =

Answer 85

...apply the exponent to each factor. (xy)³ = x³y³ (wz³)^x = w^xz^3x

Question 86

To add or subtract exponential terms with the same base... 3⁸ - 3⁷ - 3⁶=

Answer 86

pull out a common factor. (3⁶)(3² - 3¹ - 3⁰) 3⁶(9 - 3 - 1) (3⁶)(5)

Question 87

To add or subtract exponential terms with different bases... 2³ + 6³=

Answer 87

break down the bases and pull out the common factor. 2³ + 6³= 2³(1+3³)

Question 88

The square root of 16 \* the square root of 16 =

Answer 88

16

Question 89

sqr(-5)²⁼

Answer 89

sqr25 = 5

Question 90

When you square a square root vs. Square-root a square (sqr10)² vs. sqr10²

Answer 90

Get the original number vs. Get the absolute value of the original number

Question 91

sqr2 =

Answer 91

about 1.4

Question 92

sqr3 =

Answer 92

about 1.7

Question 93

sqr70 is bretween what two integers?

Answer 93

sqr64 = 8 sqr81 = 9 so between 8 & 9

Question 94

The square root of a number bigger than 1 is _______ than the original number. The square root of a number between 0 & 1 is __________ than the original number.

Answer 94

Both are closer to 1. SMALLER BIGGER1

Question 95

On the GMAT, the square root of a number is...

Answer 95

always positive. Unlike the x² which can be negative or positive.

Question 96

sqr7²²= | (two formulas)

Answer 96

sqr7²² = (7²²)^1/2 = 7^22/2 = 7¹¹ sqr7²² = sqr7¹¹ x 7¹¹ = 7¹¹

Question 97

cube root -64 =

Answer 97

-4 cube roots can be negative (unlike square roots)

Question 98

To raise a number to a fractional power... 125^2/3 =

Answer 98

Apply the numerator as is and the denominator as a root in either order. 125^2/3 = (cuberoot 125)² = 5² = 25

Question 99

To mulitply and divide square roots...

Answer 99

Multiply or devide the insides, then square-root. sqr(a) x sqr(b) = sqr(ab) sqr a / sqr b = sqr(a/b)

Question 100

When you have a sqr of a large number... sqr12 =

Answer 100

Pull the square factors out of the number under the radical sign. sqr12 = sqr(4x3) = sqr4 x sqr 3 = 2sqr3 Break the number down into primes if you don't recognize the perfect square factors.

Question 101

To add or subtract inside the root... sqr(3²+4²) =

Answer 101

Do not break apart like multiplication/division! Factor out a squre factor from the sum sqr[3¹⁰+3¹¹] = sqr[3¹⁰(1+3)] = sqr[3¹⁰(4)] = sqr[3¹⁰] x sqr[4] = 3⁵ x 2 OR (if small numbers) Follow PEMDAS under the radical and then take the square root. sqr(3²+4²) = sqr(9+15) = sqr(25) = 5

Question 102

_5⁶ x 5^4x_ 5⁴

Answer 102

5^(6+4x-4) = 5^4x+2

Question 103

-3³=

Answer 103

-27

Question 104

4³+4³+4³+4³+3²+3²+3² =

Answer 104

Factor 43 out of the first four terms and 32 out of the last three terms. 4³(1+1+1+1) + 3²(1+1+1) = 4³(4) + 3²(3) = 4⁴+3³

Question 105

sqr[24] =

Answer 105

sqr[2\*2\*2\*3] = 2sqr[2\*3] = 2sqr[6]

Question 106

To solve sqr[35²-21²]

Answer 106

Pull out the great common factor 7² sqr[7²(5²-3²)] = sqr[7²(25-9)] = sqr[7²(16)] = square root eliminated by perfect squares 7\*4 = 28

Question 107

In factions, the denominator can never equal \_\_\_\_\_\_.

Answer 107

zero.

Question 108

The larger the numerator, the _________ the fraction.

Answer 108

larger

Question 109

Which is larger? 3/5 or 4/7?

Answer 109

Corss-multiply from the bottom and across... 7x3 = 21 3/5 vs. 4/7 5x4=20 3/5 is larger.

Question 110

To simplify a fraction...

Answer 110

cancel out common fators from the numerator and demonminator. _18x_² = _6x \* 3x_ = _3x_ 60x 6x \* 10 10

Question 111

To multiply fractions...

Answer 111

first cancel any factors and then multiply the tops and bottoms together.

Question 112

The reciprocal of a negative fractions is \_\_\_\_\_\_\_\_\_\_\_\_.

Answer 112

also negative.

Question 113

To divide by a fraction...

Answer 113

multiply by the reciprocal.

Question 114

If you have addition or subtraction in the numberator of a fraction... _9x - 6_ 3x

Answer 114

Pull out a factor form the entire numorator and cancel that factor with one in the denominator. _9x - 6_ = _3(3x-2)_ = _3x-2_ 3x = 3x x

Question 115

If you have addition or subtraction in the numerator, you can rewrite...

Answer 115

the fraction as the sum of two fractions. _9x - 6_ = _3(3x-2)_ = _3x-3_ = _3x_ - _2_ = 3 - _2_ 3x 3x x x x x

Question 116

If you have addition or subraction in the denominator \_\_\_\_\_\_\_\_\_\_\_.

Answer 116

NEVER split a fraction in two. Look for a common factor on the top and bottom to simpilfy out.

Question 117

To compute "nasty" fractions...

Answer 117

put parentheses around the nasty numerators and denominators and then proceed normally.

Question 118

If you encounter a fraction within a fraction...

Answer 118

work your way out from the deepest level inside.

Question 119

To simplify sqr[18]...

Answer 119

look for the perfect squares. sqr[2\*3\*3] = 3sqr[2]

Question 120

Another word for ratio is \_\_\_\_\_\_\_\_\_

Answer 120

proporation.

Question 121

To convert a percent to a fraction....

Answer 121

write the percent "over one hundred". 45% = 45/100

Question 122

5/8 = 0.?? = ??%

Answer 122

5/8 = 0.625 = 62.5%

Question 123

7/8 = 0.?? = ??%

Answer 123

7/8 = 0.875 = 87.5%

Question 124

6/5 = ??? = ??%

Answer 124

6/5 = 1.2 = 120%

Question 125

3/8 = ??? = ???%

Answer 125

3/8 = 0.375 = 37.5%

Question 126

To calculate 0.004 \* 10^-3 =

Answer 126

Change teh negative power to postiive and divide instead of mutliply. 0. 004 \* 10^-3 = 0. 004 / 10³ = .000004

Question 127

To multiply a decimal and a big number.... 4,000,000 \* 0.0003 =

Answer 127

Move the decimal to the right in the small number and to the left in the large number. 4,000,000 \* 0.0003 = 400 x 3 = 120

Question 128

To divide two decimals... 300 / 0.05

Answer 128

move points in the SAME direction until you kill the decimals. 300 / 0.05 = 30,000 / 5 = 6,000

Question 129

When the GMAT says "what percent of", you should... What percent of 200 is 60?

Answer 129

Turn "what percent" into x/100, then multiply. x/100 \* 200 = 60

Question 130

To find percent change... If the price increases from $200 to $230, what perecent does it change?

Answer 130

divide the change in value by the original value. $30/$200 = 15%

Question 131

To find the new value after a percent change has been applied... The $60 purse was marked up by 25%

Answer 131

Find the new percent (100% + 25%), convert to a fraction (5/4) and multiply by the original value. (5/4) \* $60 = $75

Question 132

To find the percent more/less than.. $200 is what percent more than $150?

Answer 132

Divide the change in value by the original value. $50/$200 = 25%

Question 133

When you have successive percent changes... What is 120% of 150% of 30?

Answer 133

multiply the origianl value by the new percents for both percent changes. *(using fractions might allow you to cancel)* 6/5 \* 3/2 \* 30 = 54

Question 134

If you have a ratio, write it out as ________ to compute the whole. For every 2 girls in the class there are 3 boys.

Answer 134

Part : Part : Whole 2 girls : 3 boys : 7 students

Question 135

How are expressions and equations different?

Answer 135

Expressions don't have equal signs.

Question 136

4 ways to simplify expressions.

Answer 136

Combine like terms. 3x + 4x -\> 7x Find a common denominator and then combine. 3/5 + 4/10 -\>10/10 Pull out a common factor. x + xy -\> x(1+y) Cancel common factors. 3x² / 6x -\> x/2 Simplifying the expression NEVER changes its value.

Question 137

What is the order of operations?

Answer 137

Parentheses Exponents Multiplication Division Addition Subtraction

Question 138

What are two things you can do to one side of the equation but not the other?

Answer 138

Simplify the expression on one side OR Evaluate the expression on one side. You may NEVER change one expression without changing the other.

Question 139

When changing one side of an equation by multiplying, dividing, squaring or taking the square root, you must.... x + 4 = x/2

Answer 139

Put parenthesis on the other side of the equation to perform the same action to the ENTIRE other side. x + 4 = x/2 2(x+4) = (x/2)2 2x + 8 = x

Question 140

When you take the square root of an equation... x² = 49 sqr[x²] = sqr[49]

Answer 140

the equation usually splits into two separate equations. x = 7 OR x = -7

Question 141

What is x in terms of y? 7x + 4 = y

Answer 141

Means create and equation where x = something containing only y's. 7x + 4 = y -4 to both sides divide by 7 both sides x = (y-4) / 7

Question 142

To isoloate a variable deep inside an expression... 2y³ - 3 = 51

Answer 142

follow PEMDAS in reverse to undo the expression. 2y³ - 3 = 51 +3 to both sides divide by 2 both sides take the cubed root to both sides

Question 143

What is the first thing you should in an equation like this? (5x - 3) / 2x = 10

Answer 143

Get rid of the denominator. Always get vartiables out of the denominators. (5x - 3) / 2x = 10 mulitply by 2x both sides first!

Question 144

When you have variables in the exponents... 3^x = 27⁴

Answer 144

Rewrite the terms so that they have the same base, usually by breaking the bases into primes. 3^x = 27⁴ 3^x = (3³)⁴ 3^x = 3¹² x = 12

Question 145

When you have variables in the exponents, there are three bases you cannot set the exponents the same for to solve.

Answer 145

1, 0, -1

Question 146

What are the two strategies to solve a system of equations?

Answer 146

Isolate, then Subsitute OR Combine Equations

Question 147

How to do you Isolate, then Substitute to solve a system of equations. (aka subsitution) 2x - 3y = 16 y - x = -7

Answer 147

First isolate the variable you don't ultimately want. If the problem asks for x, isolate y. Isolate the variable in the equaition that's easier to deal with. y - x = -7, add x to both sides y = x -7 No replace y in the second equation with (x-7). 2x - 3(x-7) = 16 and solve for x. If you need to solve for y two, use the new value of x in the equation you created to isolate y.

Question 148

How do you kill an equation and an unknown (aka combination)?

Answer 148

If adding or subtracting the equations together will kill off a variable, it may be faster than subsitution. You may also multiply or divide the ONE ENTIRE equation to setup an expression that can be combined to eliminate a variable.

Question 149

If the system of equations have three or more unknowns... a + b - c = 12 and c - b = 8 What is the value of c in terms of a & b?

Answer 149

Isolate whatever the question asks for, and use subsitution to eliminate unwanted variables.

Question 150

What is a quadratic expression?

Answer 150

A quadratic express contains a squared variable and no higher power, such as... z² y² + y - 6 x² + 8x +16

Question 151

When dealing with quadratic equations, what is the factored form and what is the distributed form?

Answer 151

The factored form is (x+2)(x+3) = The distrubted form is x² + 5x + 6 =

Question 152

When factoring a quadratic expression, the two factors must _____ to the x coefficient and they must ____ to the constant.

Answer 152

Factors must ADD to the x coefficient and they must MULTIPLY to the constant.

Question 153

in a quadratic expression, if the constant is positive, the two numbers in the factored form must be... z² + 7z + 12 = x² - 9x +18 =

Answer 153

both positive or both negative, depending on the sign of the x term. z2 + 7z + 12 = (z+3)(z+4) x2 - 9x +18 = (x-3)(x-6)

Question 154

In a quadratic expression if the constant is negative, the factored numbers must be.. w² + 3w - 10 =

Answer 154

One number is positive and the other one is negative.

Question 155

In a quadratic expression if the constant is negative, how do you find the factor pair? ## Footnote w² + 3w - 10 =

Answer 155

First find the factor pairs of your constant that differ by the coefficent. (5 & 2). Then make one of the factors negative so they add to the correct coefficent. (5 + -2, NOT -5 + 2) Now keep the signs when you place the pair. w² + 3w - 10 = (w + 5)(w - 2)

Question 156

How do you factor this? 3x² + 21x + 36 =

Answer 156

The express is multiplied through by a common numerical factor. Pull out the common factor FIRST and then calculate normally. 3x² + 21x + 36 = 3(x² + 7x + 12) = 3(x+3)(x+4)

Question 157

How do you deal with a negative x² term? -x² + 9x + 18 =

Answer 157

Pull out the -1, which becomes a minus side outside the parentheses. - x² + 9x + 18 = - (x² - 9x + 18) = - (x-3)(x-6)

Question 158

How do you solve a quadratic expression?

Answer 158

Rearrange the equpation to make one side euqal to 0. x² + x = 6 ----\> x² + x + 6 = 0 Factor the quadratic expression. (x+3)(x-2) = 0 Set each factor equal to 0. x + 3 = 0 -\> x = -3 x - 2 = 0 -\> x = 2 Th esolution is called its roots. Only one is true at the same time.

Question 159

How do you solve a quadratic equation with squared parentheses? (y + 1)² = 16

Answer 159

Either treat (y+1) as a new variable like z. OR Take the postiive and negative square roots of 16 right away. OR FOIL (y+1)(y+1) to create a normal quadratic equation.

Question 160

How to solve a higher power quadratic formula. x³ = x

Answer 160

Solve like a normal quadratic: set the equation to zero, factor, and set factors equal to zero. Never divide by x unless you know x does not equal 0. X to the third power usually means three solutions. x³ = x x³ - x = 0 x(x²-1) = 0 x(x+1)(x-1) = 0 x = 0, -1, or 1

Question 161

If you see a quadratic expression in the numerator or denominator, try... (x² - 2x - 3) / x +1 =

Answer 161

Try factoring the quadratic expression to see if one of the factor pairs can be canceled out. (x2 - 2x - 3) = (x + 1)(x -3) cancels out with x+1 on the bottom.

Question 162

If x does not equal y, then (y-x) / (x-y) =

Answer 162

The two expressions are identical except for the sign change. (y-x) = -(x-y) Expressions that only differ by a sign change are only different by a factor of -1. If you cancel -(x-y) / (x-y) you are left with -1.

Question 163

What does the factored version of squar of a sum look like? (x+y)² =

Answer 163

x² + 2xy + y² Only one solution will be valid.

Question 164

What is the factored form of square of a difference? (x - y)²

Answer 164

x² - 2xy + y² There is only one valid soution.

Question 165

What is the factored form of difference of squares? (x + y )(x - y) =

Answer 165

x² - y² The inner and outer temes cancel the coefficent term. Square each term and subtract the difference.

Question 166

Unlike equations, inequalities have how many solutions?

Answer 166

A whole range.

Question 167

The only thing you can do to one side of an inequality and not the other is...

Answer 167

simplify. Do NOT change the value.

Question 168

What operations can you perform on a system of inequalities? What should you avoid?

Answer 168

Add or subtract from both sides. Multiply or divide both sides. If you multiply or divide by a negaive number flip the sign. You shouldn't divide by a variable unless you know the variables sign.

Question 169

Treat absolute numbers in inequalities as \_\_\_\_\_\_\_\_. |4-7| =

Answer 169

as parentheses. Solve the equation inside first and then find the absolute value of the result.

Question 170

How do you solve an equation with a variable inside the absolute value signs? 6 x |2x + 4| = 30

Answer 170

First isolate the absolute value on one side of the inequality or equation. 6 x |2x + 4| = 30 --\> |2x + 4| = 5 Set-up two equations, one negative and the other positive. 2x + 4 = 5 & -(2x + 4) = 5 --\> -2x - 4 = 5 Solve both. Get two possible values.

Question 171

How do you solve an absolute value in an inequality? |y + 3| \< 5

Answer 171

Isolate the absolute value on one side. Setup two inequalities (positive & negative). |y + 3| \< 5 --\> -y - 3 \< 5 & + y + 3 \< 5 Isolate the variable and solve both. Remember to flip the sign if you mult/divide by a negative number.

Question 172

If you know the radius of a circle, you can also find...

Answer 172

Diameter (2r) Circumference (πd) Area (π r²⁾ You can find the radius from any of these pieces of imformation too.

Question 173

What is the formula for circumference of a circle?

Answer 173

πd ~3.14 \* diameter

Question 174

What is the forumal for the area of circle?

Answer 174

π(r)² ~3.14 \* radius²

Question 175

What is a fractional portion of a circle know as? What is its portion of circumference called?

Answer 175

A sector (like a slice of pizza). Arc length.

Question 176

How do you calculate the sector area? Central angle = 45 Radius = 5

Answer 176

Figure out the faction of the circle that the sector represents. 45/360 = 1/8 1/8π5² = (25/8)π

Question 177

What are the four steps to solve a word problem?

Answer 177

1. What do they want? (write down variable = ?) 2. What do they give me? (note any relationships or specific numbers.) 3. How do I turn this information into equations? (write down the information as an equation). 4. How do I solve the quations for the desired value (use algebra).

Question 178

If you multiply two quantities that each have units... Area = 6 feet x 9 feet

Answer 178

multiply the units too. = 54 feet²

Question 179

When a problem has multiple units in it... How many hours are in two days?

Answer 179

you can cancel units in the same way numbers and variables do. 2 days \* 24/hours / 1 day = 48 hours the day units cancel each other

Question 180

How do you convert from one unit to another? How many seconds in 20 minutes?

Answer 180

Mulitiply by a conversion factor (fancy form of 1/1 with units on top and whole on the bottom) and cancel. 20 min \* (60 sec / 1 min) = 1,200 sec the minutes cancel each other

Question 181

When express rates as time and distance... It took Joe 4 hours to go 60 miles.

Answer 181

always put the time in the denominator. 60 miles / 4 hours = 15 miles per hour

Question 182

The sum of any two sides of a tringle ______ than the third side. Any side is _______ than the difference of the other two side lengths.

Answer 182

The sum of any two sides is greater than the third side. Any side is greater than the difference of the other two side lengths.

Question 183

The sum of all three interior angles of a triangle is \_\_\_\_\_\_\_.

Answer 183

180 degrees

Question 184

On a triangle, the largest angle will be across from the ________ side.

Answer 184

largest angle will be across from the longest side. like an alligator opening its mouth

Question 185

What is an isoceles triangle?

Answer 185

A triangle that has 2 equal angles and 2 equal sides.

Question 186

What is an equilateral triangle?

Answer 186

A triangle with 3 equal angles (60) and 3 equal sides.

Question 187

What is the forumula for the area of a triangle?

Answer 187

1/2 base \* height any side of the triangle can act as the base, as long as the height is perpendicular to it.

Question 188

What is a right triangle?

Answer 188

Any triangle in which one of the angles is a right angle (90 degrees).

Question 189

What is the Pythagorean Theorem?

Answer 189

a² + b² = c² For any right triangle where a & b are the legs and c is they hypotenuse.

Question 190

What are the three most common right triangles on the GMAT?

Answer 190

3-4-5 (and 6-8-10) 5-12-13 (and 10-24-26) 8-15-17

Question 191

What is a parallelogram?

Answer 191

Any 4 sided fiture in which the oppostie sides are parallel and equal. Opposite angles are also equal and the adjacent angles add up to 180 degrees. They can be divided into 2 equal triangles on the diagonal.

Question 192

How do you calculate the perimeter of a parallelogram?

Answer 192

Add the lengths of all sides. Since the opposite sides are equal you just need one of the top and side lengths to calculate this.

Question 193

How do you calculate the area of a parallelogram?

Answer 193

Base x Height

Question 194

What makes a rectangle?

Answer 194

All 4 internal angles are right angles. (It's a parallelogram with right angles.) Rectangles may be cut into two right triangles with a diagonal.

Question 195

What are the four steps to solving geometry problem?

Answer 195

1. Redraw the figures, fill in all the given information, indentify the target (make note of any equal sides/angles). 2. Identify relationships and create equations (the GMAT rarely provides extraneous info). 3. Solve the equations for the missing value. 4. Make inferences from the figures.

Question 196

What is the formula for a line in a coordinate plane?

Answer 196

y = mx + b b is the y-intercept (where the line crosses the y-axis) m = slope of the line

Question 197

How do you calculate the slope of a line?

Answer 197

rise / run = change in y / change in x

Question 198

What is the formulate for weighted average?

Answer 198

WA = (weight \* data point) + (weight \* data point) + (weight \* data point) .... / Sum of Weights

Question 199

How many arithmetic operations will the right answer require on the GMAT?

Answer 199

at least two

Question 200

When answers are spread out (and/or use the word "approximately) you can...

Answer 200

Round one number and the other one down to estimate an anwer.

Question 201

How do you figure out the ratio of a weighted average problem? Solution X at 40% strength and Y at 25% strength are mixed to create a 30% mixture. What is the ratio of the X & Y used?

Answer 201

Place 30% in the middle. X is 10 away from the middle and Y is 5 away from the middle. Swap the two. 5 X : 10 Y = 1: 2 Ratio

Question 202

How do you find the first number in a string of 5 consecutive integers with a sum of 560?

Answer 202

x + (x+1) + (x+2) + (x+3) + (x+4) = 560 5x + 10 = 560 5x = 550 x = 110

Question 203

Is 5! divisible by 5?

Answer 203

Yes! 5 \* 4 \* 3 \* 2 \*1

Question 204

What is the forumla for the sum of interior angles for any polygon?

Answer 204

(n-2) \* 180 Pentagon = 540 Hexagon = 720

Question 205

What is the formula for the area of a trapezoid?

Answer 205

[(Base1 + Base2) \* Height] / 2

Question 206

What is the formula for the area of a Rhombus?

Answer 206

(Diagonal 1 + Diagonal 2) / 2

Question 207

What is the formula for the length of the legs on an isoceles triangle?

Answer 207

45 - 45 - 90 Triangle 45 = x leg 45 = x leg 90 = x \* sqr[2]

Question 208

What is the formula for the lengths of legs on an equilateral triangle?

Answer 208

30 - 60 - 90 Triangle 30 (short) = x 60 (long) = x\*sqr[3] 90 (hyponteneuse) = 2x

Question 209

What is the formula for the diagonal of a square?

Answer 209

d = s\*sqr[2] s = side of square

Question 210

What is the formula for the diagonal of a cube?

Answer 210

d = s \* sqr[3] s = side of cube

Question 211

What is the formula for the diagonal of a rectangle?

Answer 211

h² + w² + l² = d²

Question 212

How do you calculate a central angle from the inscribed angle? inscribed angle = 45 degrees

Answer 212

Double it. 45 x 2 = 90 degree central angle

Question 213

What is the formula for surface area of a cylinder?

Answer 213

SA = 2(π \* r²) + 2π\*rh

Question 214

What is the formula for the volume of a cylinder?

Answer 214

V = π\*r²h

Question 215

On a coordinate plane, how do you find the distance between two points?

Answer 215

Draw a right triangle with the points on the hyponteneuse. Find the length of the legs by calculating rise over run. Use the pythagorean theorem.

Question 216

When a triangle is inscribed in a circle and one side of the triangle is the diameter it must be...

Answer 216

a right triangle.

Question 217

How do you know if a number is divisible by 4?

Answer 217

If it's divisible by 2 twice OR the last two digits are divisible by 4.

Question 218

How do you know if a number is divisible by 6?

Answer 218

If it is divisible by 2 and 3.

Question 219

How do you know if a number is divisible by 8?

Answer 219

If it is divisible by 2 three times or the last 3 digits are divisible by 8.

Question 220

How do you know if a number is divisible by 9?

Answer 220

If the sume of the integer's digits are divisible by 9.

Question 221

What is GCF?

Answer 221

The greatest common factor. The largest divsor of 2+ integers. If no primes in common, the GCF = 1.

Question 222

Even +/- Odd =

Answer 222

Odd

Question 223

Odd +/- Odd =

Answer 223

Even

Question 224

In multiplication, how do you know if the result will be even or odd?

Answer 224

If any integer is even = even. If all integers are odd = odd.

Question 225

If you multiply 3 even integers, the product is divisible by ?

Answer 225

2, 4, 8

Question 226

Even / Even will be ...

Answer 226

Even (12/6) Odd (12/4) Non-integer (12/8)

Question 227

Odd / Even will be...

Answer 227

Even (12/3) Non Integer (12/5)

Question 228

Odd / Even will be...

Answer 228

Non integer (9/6)

Question 229

Odd / Odd will be..

Answer 229

Odd (15/5) Non Integer (15/25)

Question 230

The algebraic representation for odds and evens is...

Answer 230

Evens = 2n Odds = 2n + 1 or 2n - 1

Question 231

An exterior angle of a triange is equal to:

Answer 231

the sum of the two non-adjacent (opposite) interior angles of the triangle.

Question 232

To divide 12.42 by 0.3

Answer 232

Move the decimal in the same direction until the divsor is a whole number. 124.2 / 3

Question 233

To raise a decimal to a power of 4 or higher: (0.5)⁴ =

Answer 233

Rewrite the decimal as the product of an integer and a power of 10: 0.5 = 5 x 10^-1 Apply the exponent to each part: (5 x 10^-1)⁴ = 5⁴ x 10^-4 Compute the first part and combine: 5⁴ = 25² = 625 625 x 10^-4 = 0.0625 Use the same method for roots of decimals (raise them a fractional power).

Question 234

How many decimal points? (0.04)³ =

Answer 234

Multiply the existing number of declimal points by the exponent. 2 places x 3 = 6 places 0.000064

Question 235

How many decimal points? cube root (0.000000008)

Answer 235

DIVIDE the number of existing decimals points by root. 9 places / 3 = 3 places 0.002

Question 236

When dealing with a ration equation. How do you simplify and solve? 4 girls / 7 boys = x girls / 35 boys

Answer 236

You can simplify vertically or horizontall but never diagonally across the equal sign. 4 girls / 1 boy = x girls / 5 boys cross multiply 4 girls \* 5 boys = x 20 girls = x