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GMAT > Quant > Flashcards

Quant Flashcards

1
Q

When I do smart numbers

A

I’ll avoid weird numbers like 0, 1 and fractions and the numbers in the problem

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2
Q

If I want to check divisibility by 9

A

I check to see if sum of digits is divisible by 9

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3
Q

What are the first 5 prime numbers?

A

2,3,5,7,11

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4
Q

What are the 6th to 10th prime numbers

A

13, 17, 19, 23 ,29

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5
Q

If I want to check divisibility by 8

A

I can divide by 2 three times
or
I can check if the last 3 digits are divisible by 8

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6
Q

If I want to check divisibility by 6

A

I need to make sure it’s divisible by 2 & 3

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7
Q

If I want to check divisibility by 4

A

I can divide by 2 twice
or
I can check if the last 2 digits are divisible by 4

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8
Q

If I want to know if a # is divisible by 3

A

I sum the digits of the number (Integers only) and check if it’s divisible

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9
Q

If N is a divisor of X & Y

A

Then N is a divisor of X + Y

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10
Q

When checking divisibility of a large number by another large number

A

I can check if it’s divisible by a factor pair of the divisor
ex 6750 div by 18
6750/2 works
and
6750/9 works
2*9=18 so it works

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11
Q

√ 2

A

approx 1.4

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12
Q

√ 3

A

Approx 1.7

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13
Q

11^2

A

121

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14
Q

13^2

A

169

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15
Q

14^2

A

196

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16
Q

15^2

A

225

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17
Q

16^2

A

256

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18
Q

25^2

A

625

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19
Q

4^3

A

64

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20
Q

5^3

A

125

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21
Q

10^3

A

1000
It is a zero per power

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22
Q

When do you Test Cases in Problem Solving?

A

You use it when the problem asks a must be or could be question

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23
Q

When do you Test Cases in Data sufficiency

A

Use it when several unknowns and it’s a Y/N question

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24
Q

x^2 - y^2=

A

(x+y) (x-y)

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25
Q

x^2 - 2xy + y^2 =

A

(x-y) (x-y) or (x-y)^2

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26
Q

x^2 + 2xy + y^2

A

(x+y) (x+y) or (x+y)^2

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27
Q

When should you use smart numbers?

A

Problem solving only for variable expressions, relative values in answers or the problem never gives a real #

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28
Q

When should you work backwards?

A

Problem solving only when answers are nice real numbers or if there is only 1 variable

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29
Q

If I see
x^2 - x < 0
or
x^2 < x

A

They both say that 0 < x < 1

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30
Q

If I see XY < 0

A

I know X and Y have opposing signs

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31
Q

If I see XY > 0

A

I know X and Y have the same sign

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32
Q

(a + b)/c =

A

a/c + b/c

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33
Q

If two denominators share a factor

A

It is faster to find the least common multiple instead of cross multiplying.
ex: 6&8 least common multiple of 24

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34
Q

-(3)^2=

A

-9

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35
Q

(-3)^2+

A

9

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36
Q

3^4=

A

81

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37
Q

x^2=16 x=

A

4^2 or -4^2

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38
Q

x^3 * x^4 =

A

x^7
always add the exponents for multiplication

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39
Q

x^3 + x^4=

A

Can only be changed through factoring
x^3(1+x)

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40
Q

(x^y)/ x^2 =

A

x^(y-2)

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41
Q

x^-2 =

A

1/x^2

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42
Q

(x^2)^4 =

A

x^8 you multiply with exponents

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43
Q

(ab)^3=

A

(a^3)(b^3)

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44
Q

(x/y)^2 =

A

(x^2)/(y^2)

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45
Q

Prime factorization of 18^3 is

A

(2^3)(3^6)

18= 29 =2(3^2)
(2*(3^2))^3= (2^3)(3^6)

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46
Q

(2^3)*(3^3)=

A

(6^3)
Only works if they have the same exponents

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47
Q

How do you estimate a root of a non perfect square ex:70?

A

Look for the perfect squares nearby and estimate
ex: 64^0.5 = 8 and 81^0.5= 9 so 70^0.5 is approx 8.5

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48
Q

What happens when you square root a number between 0 & 1?

A

You get a larger number because division by a number less than 1 and larger than 0

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49
Q

What is the main difference in cube root vs root main in regards to negativity

A

You can cube root a negative number but not normal root one.

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50
Q

8^2/3 =

A

(8^1/3)^2 = (2)^2 = 4

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51
Q

√x * √y =

A

√xy

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52
Q

√x/√y =

A

√x/y

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53
Q

When doing the radical of a large number with no obvious perfect square factor, what tool can be used?

A

Prime factorization
ex: √360= √(2 * 2* 2* 3* 3 * 5) = √((2^2) * (3^2) * 2 * 5) =2 * 3 * √10 = 6√10

54
Q

√((3^10)+(3^11)) =

A

√((3^10)(1+3)) = √(3^10) * √4 = (3^5)2

55
Q

m^(5y) * m^(y+5) =

A

m^(5y+y+5) = m^(6y +5)

56
Q

1/8 in decimal is =

A

0.125 or 12.5%

57
Q

3/8 in decimal is

A

0.375 or 37.5%

58
Q

5/8 in decimal is

A

0.625 or 62.5%

59
Q

7/8 in decimal is

A

0.875 or 87.5%

60
Q

When multiplying decimals what technique should be used

A

Multiply as if no decimals then add it in after by counting how many digits were behind the decimal originally

ex: 0.75 x 0.2 = 75 x 2 x .001=0.150
Times 0.001 cuz three behind decimals like 0.150

61
Q

How to structure a x is y% of what number?

A

Z = unknown y= in decimal
x = yz so x/y = z
ex: 16 is 2% of what number?
16 = 0.02z so 16/0.02 = z
1600/2 = z = 800

62
Q

When I see “x in terms of y”

A

I know to isolate “x” and get it in the value of “y”
ex: x= 4 + 3y

63
Q

If I see a variable is an exponent

A

I know to factor bases into primes
ex: 3^x= 27^4 -> 3^x = 3^3^4
3^x = 3^12 so x=12

64
Q

What are the 3 exceptions for bases of exponents

A

1, 0 and -1 because they always lead to the same number (except -1 which can lead to 1 or -1 depending if even or odd)

65
Q

When using the substituting method

A

I know to isolate the variable not mentioned in the question.

66
Q

When a question asks for “x+y =”

A

I don’t need to find each individual solution just the combined x+y value

67
Q

When I come across a difficult multiplication like 102*301

A

I know I can distribute the multiplication using foil
ex: (100 + 2) * (300 +1)
= 30,000 + 100 + 600 + 2
= 30,702

68
Q

When I see a quadratic with a number before the x^2
ex: 2X^2 4x + 4

A

I know to first factor out the number and then tackle the quadratic. Same thing for a minus sign as well
Ex: 2( x^2 + 2x + 2)

69
Q

If I see a problem like x^2 = 4

A

I know to square root both sides and use the negative and positive results
Ex: x = 2 & x= -2

70
Q

When I see a hard square like 306^2

A

I know I can do:

300^2 + 2 * 300 * 6 +6^2

Because of (a+b)^2 = a^2 + 2ab + b^2

71
Q

When I want to do percent larger

A

I know to use the formula ((a-b)/b) * 100

72
Q

When I see a straight line

A

I know its the shortest distance between two points

73
Q

when I see two or more intersecting lines

A

I know their middle angles add up to 360

74
Q

When I see two lines intersect I know the angles opposite

A

are equal to each other. aka Vertical Angles

75
Q

When a transversal line cuts through two parallel lines

A

I know the angles are the same for both lines

76
Q

I know that when you add any acute angle with any obtuse angle

A

That both angles add to 180 degrees

77
Q

When I see the symbol ||

A

I know the lines mentioned are parallel
ex: MP ||AB

78
Q

When I see a parallelogram

A

I know that the opposite sides and opposite angles are equal

79
Q

When I see a shape with 4 sides

A

I know the angles inside add to 360 degrees

80
Q

When I see a shape with 5 sides

A

I know the angles add to 540 degrees

81
Q

When I see a shape I know I can calculate the amount of angles with

A

(n - 2) * 180 where n = amount of sides

82
Q

When I cut a 4 sided shape with a line connecting opposite sides

A

I know it makes two triangles with 180 degrees each

83
Q

To get the area of a trapezoid

A

I know to do (B1+B2)/ 2 * height

84
Q

To get the area of a parallelogram

A

I know to do Base * Height

85
Q

When I see a question asking for the surface area of all faces

A

I know it’s asking for the sum of all faces

86
Q

When someone is asking for the surface area of a cube or rectangular solid

A

I know it has 6 faces

87
Q

Volume for a 4 sided object is:

A

Length * Width* Height

88
Q

When I’m asked about fitting a 3D object into another 3D object

A

I know that knowing the volume of each is not enough. It depends on dimension

89
Q

When trying to find the third side of a right sided triangle

A

I know to use the Pythagorean Theorem

a^2 + b^2 = c^2

90
Q

When I see two sides of a triangle are equal

A

I know that their angles are also equal

91
Q

Triangles sides are bounded by what two restraint

A
  1. A side of a triangle can’t be more than the sum of the two other sides.
    (t1+t2) > t3 regardless of which side!!
  2. A side of a triangle can’t be less than the sum of the difference of the other two sides
    (t1- t2) < t3 regardless of which side!!
92
Q

Every right triangle is composed of what?

A

Two legs (a & b) and a hypotenuse (c)

The right angle is formed by the legs a & b

93
Q

When I see a triangle with two of the sides 3 - 4 - 5

A

I know it’s a right triangle.
9 + 16 = 25 for the Pythagorean theorem

Multiples include:
6 - 8 - 10
9 - 12 -15
12 - 16 -20

94
Q

When I see a triangle with two of the sides 5 - 12 - 13

A

I know it’s a right triangle with the values:
25 + 144 = 169 for the Pythagorean theorem

Multiples include:
10 -24 -26

95
Q

When I see a triangle with two of the sides 8 - 15 -17

A

I know it’s a right triangle with the values:
64 + 225 = 289 for the Pythagorean theorem

96
Q

When I see a triangle with two of the three sides equal that has a right angle

A

I know its a 45 - 45 - 90 triangle

97
Q

When I see a 45 - 45 - 90 triangle

A

I know I can find the sides through this formula:

Leg : Leg : Hypotenuse
x : x : x√2

98
Q

When I see a square with a given diagnoal

A

I know I can use the 45 - 45 - 90 ratio to find the sides of the square which are equal to the leg of the
45-45-90

99
Q

When I see a equilateral triangle (all 3 same sides) cut in the middle to form two other triangles

A

I know it turns into two 30 - 60 - 90 triangles

100
Q

When I see a 30 - 60 - 90 triangle

A

I know I can find the sides using this ratio

Leg : Leg : Hypotenuse
30° : 60° : 90°
x : x√3 : 2x

101
Q

When I see a exterior angle of a triangle

A

I know I can find the interior angel through
180° - exterior angle = interior angle

I also know that the two other interior angles = to the exterior angle

102
Q

When I think about the base of a triangle

A

I know it’s important to remember that each side of a triangle can be the base

103
Q

When I see a triangle that the sides are multiples of each other

A

I know that they have the same angles

104
Q

When I see triangles with the same angles

A

I know that they are multiples of each other

105
Q

When I see a line pass through the center of a circle

A

I know it’s the diameter of the circle

106
Q

When I have the radius of the circle

A

I know I can find the diameter, circumference and area of a circle

107
Q

What are the formulas of a circle if radius is equal to r

A

Radius = r
Diameter = 2r
Circumference = 2 * r * π
Area = π * r^2

108
Q

When I need to estimate a value with π

A

I make π = 3

109
Q

When I see a center angle and an inscribed angle

A

I know the inscribed angle is equal to 1/2 of the center angle.

110
Q

If I see an inscribed triangle where one side is the diameter

A

I know that the triangle must be a right triangle

111
Q

When I see a question involving quadrants on a coordinate plane

A

I know the quadrants are ordered as follows:

Q2|Q1
Q3|Q4

112
Q

I know that if I have two points on a line and I want to find the slope

A

I need use the formula

Rise/Run or (y2-y1)/(x2-x1)

It is not important which point is x1 or x2 as long as it’s consistent

113
Q

When I see a question asking for an x intercept

A

I know it’s the point where y = 0

114
Q

When I see a question asking for a y intercept

A

I know its the point where x = 0

115
Q

When I see it’s a linear equation

A

I know it cannot have terms such as x^2, √x or xy

116
Q

Linear equations are usually represented in the following form

A

y = mx + b

Always reorganize to isolate y

117
Q

When I see an angle BAC

A

I know that A is the mid point

118
Q

When X & Y are positive , if 3x < 2y

A

Then x < y and same goes for other situations where the larger quantity has the smaller multiplier

119
Q

When I want to check divisibility by 11 in a 3 digit number

A

I know to see if the hundred digit and the single digit summed equal the tens digit.

ex: 165/11 = 15

1 + 5 = 6

120
Q

When I have a 3 set problem

A

I know to use the formula:

Total = Group A + Group B + Group C - (AB) - (BC) - 2(ABC)

121
Q

What is 1/11 in decimals

A

0.0909090

122
Q

What is 2/11

A

0.1818

123
Q

What is 3/11

A

O.272727

124
Q

4/11

A

0.3636

125
Q

How do I find x/11 if x = 1 to 10

A

= to 0.9x repeating

Ex: 8/11 = 0.72727

10/11 = 0.9090

126
Q

2^5

A

32

127
Q

2^6

A

64

128
Q

4^3

A

64

129
Q

3^4

A

81

130
Q

1/6 in percent is

A

16.66% or 16&2/3%

131
Q

1/9 in decimals is

A

0.11111

132
Q

What happens if you add 1 to both the numerator and denominator of a fraction

A

The fraction gets closer to 1

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