Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

GMAT > Math Techniques > Flashcards

Math Techniques Flashcards

1
Q

GCF and LCM

A
  1. Prime Factor
  2. Create box with all unique factors across top, two rows (one for each number)
  3. Input unique factors with correct exponents
    4a. GCF - Multiply lowest values in each column
    4b. LCM - Multiply highest values in each column
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Converting Decimal to a Fraction

A

Place the number over 1*10^number of digits in the number.

.123 = 123/1000

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Arc Length Calculation

A

Inner angle / 360 = arc length / circumference

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Disguised 3-4-5 Right Triangle

A

30-40-50
60-80-100

Etc.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Sides-to-Degrees Calculation

A

(n-2)(180)

Where n is the number of sides of the shape

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Combining Ratios

A

Combine ratios by multiplying or dividing common elements of the two ratios to get a common factor or multiple.

A:B = 5:6
B:C = 8:9
A:C = 2:3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Is x prime?

A

Test divisibility rules on primes less than square root

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Area of an Equilateral Triangle

A

(√3 / 4)(side^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

x + y Divisibility

A

If x and y are both divisible by d, then (x + y) is divisible by d

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Negative Exponents

A

Turns the base into a reciprocal, does NOT change the sign of the base.

1 / 2^(-3) = 2^3

2^(-5) = 1 / 2^(5)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Mixed Roots

A

Can compare size / manipulate by multiplying to square of coefficient, then moving coefficient under the root.

2√13 = (√4)(√13) = √4*13 = √52

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Parallel Symbol

A

A ∥ B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Standard Deviation

A

Never need to calculate

  1. Larger spaces = wider standard deviation
  2. All constituents of a set shifted by the same interval? No change to standard deviation
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Normal Distribution

A

1st St. Dev = ~34% on either side
2st St. Dev = ~14% on top of 1st St. Dev
3st St. Dev = ~2% on top of 2st St. Dev

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Terminating Decimals

A

Factor out 2s and 5s in denominator - any other factors and it will not terminate

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Functions f(x)

A

Just plug and play

f(x) = x^2 and g(x) = x+3
f(g(1)) = 16

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Rectangle

A

A square is a rectangle, but a rectangle is not necessarily a square. Length is defined as the longer side.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

x^2 = 9

A

x = 3 OR -3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Circumference of a Circle

A

2πr

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Colinear

A

Two points that lie on the same straight line. Any two points are colinear, three points may or may not be colinear.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Rate / Time Problems

A

Going opposite directions? Add rates. Then plug into R*T = D

Going the same direction? Subtract rates

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Multiplying Decimals

A

Multiply the decimals by 10^x and then pull back out when finished. Can do with fractions as well.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Simplifying Factorials

A

9! / 6! = (9)(8)(7)(6!) / 6! = (9)(8)(7)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Can’t do the math? Shouldn’t do the math?

A
  1. Estimate
  2. Backsolve
  3. Use your own numbers
  4. Get creative
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

(w / x) / (y / z)

A

(w / x)(z / y)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Distance Formula

A

Rate * Time = Distance

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Adding or Subtracting Exponents

A

23^13 - 23^12

Can ONLY factor, cannot subtract because these are not like terms

(23^12)(23-1) = (23^12)(22)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Percentages

A

is / of = % / 100

Set equal to each other and cross multiply

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

Right Triangle

A

a^2 + b^2 = c^2 applies

“Legs” are the shorter sides, not the hypotenuse

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Percent Change

A

(New - Old) / Old

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

Semi-circles

A

If you take any point on a semicircle’s curved edge and draw lines to the corner points, it creates a 90 degree right triangle, with the diameter as the hypotenuse

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

If a is divisible by b, and b is divisible by c…

A

a is also divisible by c

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

If d has e and f as prime factors, then…

A

d is divisible by e, f, and (e)(f)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

Every factor of a number (except 1)…

A

Is a product of a different combination of the number’s prime factors

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

Quadrilateral

A

360 degrees
Area of a Trapezoid = ((Base 1 + Base 2) / 2 )(Height)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

Data Sufficiency Answers

A

A: Only I is sufficient
B: Only II is sufficient
C: I and II are only sufficient TOGETHER
D: I and II are both sufficient ALONE
E: I and II are NOT sufficient TOGETHER

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

Divisibility Rules: 4

A

If the final two digits of a number are themselves divisibly by 4, then the number is divisible by 4. 104, 288, 312

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

Is Zero negative or positive?

A

Neither - it is a neutral integer

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

Area of a circle

A

πr^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

3D Boxes

A

Vertices = Corners
Faces = Sides
Split into planes to find area, volume, etc.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

Simple Permutations

A

How many ways can n items be ordered? n!

Repeat entities? Divide n by # of repeats (x repeats, divide by x!) 3 repeats? Divide by 3!, or 6

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
42
Q

Sum of Consecutive Numbers

A

(n/2)(First number + Last Number)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
43
Q

Exponent Rules (Addition or Subtraction)

A

Bases (even if the same) cannot be added or subtracted if the exponent values are different, because they are not like terms. Can factor out the bases though.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
44
Q

Adding or Subtracting Fractions

A

Simply multiple the denominators to get a common denominator and the numerators accordingly to get add or subtract.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
45
Q

Percentage Change Calculation

A

(New - Old) / Old

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
46
Q

Three Overlapping Sets

A

Draw Venn Diagram, always subtract out center groups

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
47
Q

Arc Length Formula

A

(Center Angle / 360) = (Arc Length / Circumference)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
48
Q

Divisibility Rules: 6

A

Must be divisible by 2 and 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
49
Q

Sides of a 45-degree right triangle

A

x, x, x√2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
50
Q

Range

A

Largest value in a set minus the smallest value

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
51
Q

Exterior Angles

A

Sum of opposite interior angles in a triangle is equal to the exterior angle opposite the third angle - look at flash card for diagram

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
52
Q

Parallelogram

A

A shape consisting of two sets of parallel lines, angles opposite each other are equal. Area = base*height

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
53
Q

Divisor

A

All the factors of a number and their negative counterparts

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
54
Q

(√x)(√y) =

A

√xy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
55
Q

(√x) / (√y) =

A

√(x/y)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
56
Q

√x + √x =

A

2√x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
57
Q

√x + √y =

A

Nothing can be done to simplify here

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
58
Q

(a / b)(c / d) =

A

ac/bd

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
59
Q

The b root of x^a =

A

x^(a/b)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
60
Q

Inequalities

A

When dividing or multiplying by a negative number, the sign flips - may have to test multiple scenarios! All other operations by negatives, or positives do not flip sign

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
61
Q

Area of a Triangle

A

1/2 * base * height

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
62
Q

Compounded Percents

A

Calculate as several percent changes at a time

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
63
Q

5-12-13 Right Triangle

A

May be disguised by proportional multiples

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
64
Q

Divisibility Rules: 2

A

Any even number is divisible by 2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
65
Q

Trapezoids

A

Area of a trapezoid = ((Base 1 + Base 2)) / 2) * Height

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
66
Q

Addition Method

A

Multiply an equation within a system of equations to get rid of one of the variables, then can add together to solve for the other variable

Can also subtract! Same effect

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
67
Q

Substitution Method

A

For solving systems of equations. Solve for one variable in terms of the other, then plug the result into the other equation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
68
Q

Even Exponent?

A

The solution to x^2 = 9 could be 3, OR -3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
69
Q

Quant Problem Solving Strategies

A
  1. Estimate
  2. Backsolve
  3. Use Your Own Numbers
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
70
Q

Sum of Equally Spaced Numbers

A

(Avg. of #s)(# of #s)

(Avg. of #s) = (Biggest + Smallest) / 2

(# of #s) = (Biggest - Smallest) / Spacing

Negative to positive? Cancel out corresponding additions on either side - -23 + 23 = 0, for instance

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
71
Q

Favorite Probability Trick

A

Find the probability of what you’re NOT supposed to be solving for, and subtract it from 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
72
Q

Data Sufficiency Danger Areas

A
  1. Negative Numbers
  2. Even Exponents
  3. Non-Integers
  4. Inequalities with Variables - don’t know sign, may not know direction of inequality symbol
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
73
Q

Sub-Divided Group

A

Draw a visual tree diagram, use 100 as a base if working with percentages

74
Q

Multiplying Fractions

A

(a/b)*(c/d) = ac/bd

75
Q

Dividing Fractions

A

Multiply by reciprocal

(a/b) / (c/d) = ad/bc

76
Q

GCF Facts

A
  1. The GCF of two numbers may be 1, as in the case of primes
  2. GCF can also be one of the two numbers, as in the case of 6 and 12
77
Q

Similar Triangles

A

Triangles that have the same angles but different sizes have proportional perimeters and areas

78
Q

Is 1 prime?

A

No

79
Q

Divisibility Rules: 3

A

If the sum of the digits of a number sum to 3, then the number is divisible by 3

80
Q

(Even)(Even) =

A

Even

81
Q

(Even)(Odd) =

A

Even

82
Q

(Odd)(Odd) =

A

Odd

83
Q

Even +/- Even =

A

Even

84
Q

Even +/- Odd =

A

Odd

85
Q

Odd +/- Odd

A

Even

86
Q

What to do if forget Even/Odd rules

A

Use 2 and 3 - all numbers, even negatives, behave the same way

87
Q

(y^a)(y^a) =

A

(x*y)^a

Usually working backwards to find prime bases

88
Q

(x^a)(x^b) =

A

x^(a+b)

89
Q

(x^a)^b =

A

x^(ab)

90
Q

x^a^b =

A

x^(a^b)

91
Q

(x^a)/(x^b) =

A

x^(a-b)

92
Q

Difference of Squares

A

x^2 - 16 = (x+4)(x-4)

May need to manipulate expression to get a difference of squares

93
Q

Equivalent Equations

A

Set equations equal to the same value equal to each other, then can solve through substitution or addition. Can manipulate to make equations equivalent.

94
Q

Absolute Values

A

Keep track of negatives - try to backsolve

95
Q

Quadratic Equation Terms

A

x^2 + 7x + 12 = 0

  1. Factors: (x+3)(x+4) = 0
  2. Roots (Solutions): x = -3 or x = -4
96
Q

Difference of Squares - General Formula

A

x^2 - y^2 = (x-y)(x+y)

97
Q

Is 0 an integer?

A

Yes

98
Q

Positive Square Root Rule

A

Any time you see a square root in the GMAT, assume only the positive square root - can NOT be the negative square root

99
Q

Conjugate

A

The conjugate of (x-√2) is (x+√2) - multiply denominators by these to get denominator off the bottom of fractions, GMAT does not like irrationals in the denominator

100
Q

Work / Rate Reciprocal Rule

A

If we add machine rates together to find how much of the job they can complete in one hour, we can flip result to see how many units of time to complete job.

101
Q

Formula for number of integers between x and y, inclusive

A

y-x+1 - Can use to find number of multiples between two numbers as well

102
Q

Multiples of 5 between 358 and 81?

A

85 = 517
385 = 571

71-17+1 = 55

103
Q

Rational Substitution

A

y - 13√y + 36 = 0

Substitute u for √y and solve

u^2 - 13u + 36 = 0

104
Q

(a-b)^2 =

A

a^2 + b^2 - 2ab

105
Q

(a+b)^2 =

A

a^2 + b^2 + 2ab

106
Q

(a+b)(a-b)

A

a^2-b^2

Difference of Squares

107
Q

Extraneous Roots

A

If roots are the answer to a data sufficiency equation, CHECK BOTH ROOTS by plugging back in - if one does not work, it is an extraneous root and is NOT a solution

108
Q

Calculate the number of divisors

A

Prime Factor, then add 1 to exponents and multiply exponent values.

Looking for odd factors, or even factors? Sam process, but with only odd or even prime factors

109
Q

Is a number a prime number?

A
  1. Cannot be >2 and even
  2. Not divisible by 3
  3. Not divisible by 5
  4. Not divisible by 7
110
Q

Decimal Addition or Subtraction

A

Line up decimal points and add

111
Q

Decimal multiplication

A

Product will have same total number of decimals as the sum of the decimal points of both factors

112
Q

Decimal Division

A

Multiply top and bottom by the same 10^x to get whole numbers, then divide

113
Q

Equilateral Triangle

A

Regular Triangle, all sides same length, all angles = 60 degrees.

Often need to bisect into two 30, 60, 90 right triangles.

114
Q

Sides of a 30-60-90 Right Triangle

A

x, x√3, 2x

115
Q

To Remember: Angles

A
  1. When lines intersect, angles on same side add to 180 degrees
  2. All angles in a parallelogram are the same if they face each other
116
Q

Complex Combinations

A

Think total - options that don’t work, or one way that works * number of options

117
Q

Circumference of a Circle

A

2πr

118
Q

Integer

A

Any whole number, including 0

119
Q

Units Digit Multiplication

A

Just multiply the units digit to find what the units digit will be. Typically works in patterns for large exponents

120
Q

Average Rate or Speed Calculation

A

TOTAL Distance / TOTAL time

May need to find totals first

121
Q

Cubed Roots

A

As with square roots, find prime factors and reduce by triple occurrences under the root symbol

122
Q

Divisibility Rules: 8

A

If the last three digits are themselves divisible by 8, then the number is divisible by 8. 6,216 = 216/8 = Yes

123
Q

Divisibility Rules: 9

A

If the digits sum to something divisible by 9, the number is divisible by 9 and 3

124
Q

Divisibility Rules: 7

A

No clean rule - long division

125
Q

Proportion

A

Ratios or fractions that are equal to each other. Cross multiply and divide.

126
Q

Things to Remember: Scientific Notation

A

Just two things multiplied together, can reduce or split apart as need be

127
Q

Calculation for slope of a line

A

Rise / Run

128
Q

Negative Exponents

A

Just take reciprocal and make exponent positive - do not change the sign of the base! If part of a product, can move it to top or bottom of a fraction if needed

129
Q

Composite Numbers

A

Any number that is composed of multiple primes factors

130
Q

Probabilities: And vs. Or

A

And: Multiply
Or: Add

131
Q

Circles: Interior Angles

A

Triangles from the center have radius as sides, so makes an isosceles triangle

132
Q

Divisor

A

All the factors of a number and a their negative counterparts

133
Q

Area of a Circle

A

πr^2

134
Q

Rate / Time Questions

A

Find a common time period if working together - use fractions to get to same denominator of time, then add or subtract as needed

135
Q

Compound Interest Calculation

A

Usually don’t need to calculate:

Principle(1+(Interest Rate/# of Periods per Year))^((# of Periods per Year)(# of Years))

136
Q

Scientific Notation

A

Can move decimal back and forth by changing the 10^x exponent. Can split the factors up as well if needed

137
Q

Line Slope Properties

A

Parallel lines have the same slope, perpendicular lines have negative reciprocal slopes

138
Q

Area of a Trapezoid

A

((Base 1 + Base 2) / 2) * Height

139
Q

Convert a Fraction to a Decimal

A

Long Division

140
Q

Basic Concepts: Geometry

A
  1. Do NOT trust the diagram
  2. Geo problems are susceptible to estimation
  3. Always be looking to extend lines or subdivide shapes if needed
141
Q

Bisection

A

To divide something exactly in half

142
Q

Polygons: Interior Angles Total Calculation

A

(n-2)*180, where n is the number of sides

A “Regular” polygon is one that has sides of all the same length and all the same angels

143
Q

Volume of a Cylinder

A

Find area of circle on top/bottom, then multiply by height

144
Q

Perpendicular

A

⊥, negative reciprocal slopes

145
Q

No order in smaller group

A

n! / (n-k)!(k!), where n is the total number in the group and k is the smaller number being chosen

146
Q

Properties of a Square

A

A quadrilateral, four 90-degree angels, all sides same length.

Can bisect into two 45-degree right triangles

147
Q

Arc Length Formula

A

(Center Angle / 360) = (Arc Length / Circumference)

148
Q

Basic Probabilities Calculation

A

Acceptable Outcomes / Total Possible Outcomes

Always between 0 and 1

149
Q

Isosceles Triangle

A

Triangles in circles are isosceles, if the center is at an angle - 2 sides are radius

150
Q

Divisibility Rules: 5

A

Ends in a 0 or a 5

151
Q

Hexagon

A

6 sides, (6-2)(180) = 720 total interior degrees

152
Q

Order in Smaller Group

A

n! / (n-k)!

153
Q

Perfect Square

A

The square of an integer

154
Q

Perfect Cube

A

The cube of an integer

155
Q

Shortcut for Addition or Subtraction

A

Do math for just units digit - is that enough to narrow it down to one answer?

156
Q

Simplify…

A

…before you multiply

157
Q

Prime #: # of Factors

A

2

158
Q

Square of Primes: # of Factors

A

3

159
Q

Composite Number: # of Factors

A

4 or more

160
Q

First Several Primes

A

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

161
Q

When two numbers DONT share any prime factors…

A

Their LCM is always their product

162
Q

When two numbers DO share prime factors…

A

Their LCM is less than their product - you have to strip out any common factors

163
Q

if x is divisible by a and b, then…

A

…x is divisible by the LCM of a and b

This means if asked if a certain number MUST be divisible by another, it’s really an LCM question

164
Q

Two factors of x with Primes in common?

A

Combine, eliminating any overlap in prime factors to find the LCM

165
Q

Two factors of x with no primes in common?

A

The LCM is the product of those numbers

166
Q

Negative Number raised to an even power

A

Always positive

167
Q

Negative Number raised to an odd power

A

Always negative

168
Q

Even Exponents…

A

…Hide the Sign of the base

169
Q

Negative Exponents

A

Creates a reciprocal value with a positive exponent. You can move multiplied terms above or below division lines by changing sign of the exponent. Negative exponents do NOT change the sign of the base.

170
Q

When a positive power to a negative power…

A

Multiply the exponents - you now have a negative exponent

171
Q

Square of a Sum

A

(x + y)^2 = x^2 + 2xy + y^2

172
Q

Square of a Difference

A

(x - y)^2 = x^2 - 2xy + y^2

173
Q

Difference of Squares

A

(x + y)(x - y) = x^2 - y^2

174
Q

(y - x) / (x - y)

A

GMAT Disguise - factor out -1 from top or bottom to get factors you can simplify

175
Q

Quadratics in Fraction?

A

Factor and Cancel! Avoid fractional coefficients at all costs

176
Q

When should you divide by a variable?

A

Only if you are SURE the variable is not 0

177
Q

Quadratics with higher powers?

A

Factor out variable, then treat as third factor

x^3 - 3x^2 + 2x = 0
x(x^2 - 3x + 2) = 0
x(x - 2)(x - 1) = 0
Roots are 0, 1, and 2

178
Q

Substitution (y + 1)^2 = 16

A

Substitute u for (y + 1)
u^2 = 16
u = 4 or -4
y + 1 = 4
y + 1 = -4
Solve

179
Q

Quadratic Roots

A

Roots are possible solutions, but the variable is not equal to both simultaneously

180
Q

Simplify Quadratics before factoring

A

Roots are answers to factors, not simplified coefficient

3(x + 3)(x+4)
x = -3, -4

181
Q

Multiplication FOIL

A

(102)(301) = (100)(300) + (100)(1) + (2)(300) + (2)(1)

Allows you to work with easier numbers

182
Q

If you have a variable in an exponent…

A

Make bases the same to solve equation. Usually must prime factor bases and then get equal to each other through exponent rules

2^y = 2^4
y = 4

Exceptions are bases of 0, 1, or -1

GMAT (6 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions