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Iman's GMAT Quant > Quant - 1 > Flashcards

Quant - 1 Flashcards

1
Q

Reciprocal x

rɪˈsɪprəkəl

A

1/x

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2
Q

Prime numbers less than 100

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51, 53, 59, 61, 67, 71, 73, 79, 89, 97

کلا ۲۵ تاس
۱۵ تا زیر ۵۰
۱۰ تا بالای ۵۰

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3
Q

Finding number of factors in a particular number

A

Step 1: Find the prime factorization of the number
Step 2: Add 1 to the value of each exponent. Then multiply these results.

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4
Q

Finding the LCM

Lowest Common Multiple

A

Step 1: Find the prime factorization of the number
Step 2: Of any repeated prime factors among the integers in the set, take only those with the largest exponents.

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5
Q

Finding the GCF

Greatest Common Factor

A

Step 1: Find the prime factorization of the number
Step 2: Of any repeated prime factors among the integers in the set, take only those with the smallest exponents.

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6
Q

LCM (x,y) * GCF (x,y)

A

x * y

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7
Q

Perfect square 1 to 15

A

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

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8
Q

Perfect cube 1 to 10

A

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

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9
Q

Which one is bigger
X, X2, √X

0 < X < 1

A

X2 < X < √X

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10
Q

Prime numbers less than 10

A

2, 3, 5, 7

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11
Q

Prime numbers between 10 to 20

A

11, 13, 17, 19

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12
Q

Prime numbers between 20 to 30

A

23, 29

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13
Q

Prime numbers between 30 to 40

A

31, 37

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14
Q

Prime numbers between 40 to 50

A

41, 43, 47

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15
Q

Prime numbers between 50 to 60

A

53, 59

51 is divisible by 3, 17

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16
Q

Prime numbers between 60 to 70

A

61, 67

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17
Q

Prime numbers between 70 to 80

A

71, 73, 79

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18
Q

Prime numbers between 80 to 90

A

83, 89

87 is divisible by 3, 29

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19
Q

Prime numbers between 90 to 100

A

97

91 is divisible by 7 and 13

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20
Q

Divisibility rule

2

A

if the ones digit is 0, 2, 4, 6, 8

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21
Q

Divisibility rule

3

A

Sum of all digits must divisible by 3

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22
Q

Divisibility rule

4

A

Last two digits must divisible by 4

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23
Q

Divisibility rule

5

A

Last digit is 0 or 5

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24
Q

Divisibility rule

6

A

It shoud both divisible by 2 and 3

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25
Q

Divisibility rule

8

A

Last three digits should divisible by 8

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26
Q

Divisibility rule

9

A

Sum of all digits should divisible by 9

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27
Q

Divisibility rule

11

A

A Number divisible by 11 if the sum of odd-numbered place digits minus the sum of even-numbered place digits is divisable by 11.

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28
Q

Trailing Zeros

A

Is the number of (2x5) pairs in prime factorization

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29
Q

Leading Zeros in a Decimal

1/X

A

If X is and integer with k digits, then 1/X have k-1 leading zeros
unless:
X is a perfect power of 10, in which case there will be k-2 leading zeros.

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30
Q

Terminating decimal

A

The decimal equivalent of a fraction will terminate if and only if the denominator of the reduced fraction has a prime factorization that contains only 2s and 5s, or both

  • 1/12=0.0833333…
  • 1/20=0.05
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31
Q

Two consecutive integers

A

Will never share any prime factors. Thus, the GCF of two consecutive integers is 1.

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32
Q

Perfect square

11

A

121

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33
Q

Perfect square

12

A

144

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34
Q

Perfect square

13

A

169

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35
Q

Perfect square

14

A

196

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36
Q

Perfect square

15

A

225

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37
Q

Perfect cube

2

A

8

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38
Q

Perfect cube

3

A

27

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39
Q

Perfect cube

4

A

64

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40
Q

Perfect cube

5

A

125

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41
Q

Perfect cube

6

A

216

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42
Q

Perfect cube

7

A

343

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43
Q

Perfect cube

8

A

512

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44
Q

Perfect cube

9

A

729

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45
Q

√2

A

1.41

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46
Q

√3

A

1.73

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47
Q

√6

A

2.45

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48
Q

√7

A

2.65

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49
Q

√8

A

2.83

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50
Q

√10

A

3.16

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51
Q

√5

A

2.24

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52
Q

Bases of 2

A
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53
Q

Bases of 3

A
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54
Q

Bases of 4

A
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55
Q

Bases of 5

A
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56
Q
A
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57
Q
A
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58
Q
A
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59
Q
A
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60
Q
A
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61
Q
A
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62
Q
A
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63
Q
A
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64
Q
A
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65
Q
A
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66
Q
A
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67
Q
A
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68
Q
A
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69
Q

|a+b| relation with |a|+|b|

A

This is always true:
|a+b|≤|a|+|b|

When |a+b|=|a|+|b|, this means:

  • One or both quantities are 0
    Or
  • Both quantities have the same sign.
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70
Q

|a-b| relation with |a|-|b|

A

This is always true:
|a-b|≥|a|-|b|

When |a-b|=|a|-|b|, this means:

  • The second quantity is 0
    Or
  • Both quantities have the same sign and the absolute value of |a-b| is greater than or equal to absolute value of |a|-|b|.
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71
Q

Translation

is

A

=

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72
Q

Translation

was

A

=

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73
Q

Translation

has been

A

=

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74
Q

Translation

more

A

+

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75
Q

Translation

years older

A

+

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76
Q

Translation

years younger

A

-

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77
Q

Translation

less

A

-

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78
Q

Translation

times

A

x

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79
Q

Translation

less than

A

-

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80
Q

Translation

fewer

A

-

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81
Q

Translation

as many

A

x

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82
Q

Translation

factor

A

x

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83
Q

Translation

of

A

x

84
Q

Price per item

A

(Total cost)/(Number of items)

85
Q

Profit

A

Total revenue - Total cost
or
Total revenue - [Total fix costs + Total variable costs]

86
Q

Simple interest

A

Principale x Rate x Time

87
Q

Compound Interest

A

A: Future value
P: Principale
r: rate of interest
n: number of times per year interest is compounded
t: times in years

88
Q

Linear growth formula

A

Fn: Final growth
p: initial value
n: n (th) growth period
k: constant increase during each period

89
Q

Formula

Rate - Time - Distance

A
90
Q

Formula

Average rate

A
91
Q

Formula

Converging/Diverging Rate

A
92
Q

Formula

Round-Trip Rate

A
93
Q

Formula

Catch-Up Rate

A
94
Q

Formula

Catch-Up and Pass

A
95
Q

Formula

Combined worker

A
96
Q

Translation

Percent of

A

“Percent of” means to multiply a given percent by a given value

97
Q

Translation

What percent of

A
98
Q

Translation

Percent less than

A
99
Q

Translation

Percent greater than

A
100
Q

Translation

x is n percent of y

A
101
Q

Formula

Percent change

A
102
Q

Number of members in either set

A or B

A

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

103
Q

Three circle venn diagram equations

A
104
Q

In three circle venn diagram

What is the total # of unique members?

When the unique items is known

A

[A only+B only+C only] + [#(A and B) only) + #(B and C) only + #(A and C) only] + #[(A and B and C)] + #[Neither A nor B nor C]

105
Q

In three circle venn diagram

What is the total # of unique elements?

When the unique items is unknown

A

in (Group A) + #in (Group B) +#in (Group C) - #in (Groups of exactly two) - 2 #in (Group of exactly three) + #in (Neither)

106
Q

In three circle venn diagram

Where is only A

A
107
Q

In three circle venn diagram

Where is A and B and C only

A
108
Q

In three circle venn diagram

Where is neither A nor B nor C

A
109
Q

In three circle venn diagram

Where is intersection of Group B and Group C

A
110
Q

In three circle venn diagram

Where is A and B only

A

(A and B) only = #(A and B) - #(A and B and C)

111
Q

Defecit

ˈdefəsət

A

an excess of expenditure or liabilities over income or assets in a given period

کسری بودجه

112
Q

Profit and Cost expression

A

%profit = 100 x (profit/cost)

113
Q

Profit Margin

A
114
Q

The Avg is 30, it would go up by 50
What is the new Avg?

A

30 + 50 = 80

115
Q

Quadrupeled

kwäˈdro͞opəld

A

x 4

116
Q

If a ≤ x ≤ b and c ≤ y ≤ d what is the Max value of xy

A

will be largest amount amount among ac, ad, bc and bd

117
Q

If a ≤ x ≤ b and c ≤ y ≤ d what is the Min value of xy

A

will be smallest amount among ac, ad, bc and bd

118
Q
A

… we know the sign of the variable

119
Q

Evently spaced sets

A
  • {4, 5, 6, 7, 8, 9, 10, 11}
  • {3, 5, 7, 9, 11}
  • {5, 10, 15, 20, 25, 30}
120
Q

Counting the number of integers in a set of consecutive integers (inclusive)

A

Highest number - Lowest numbers + 1

121
Q

Counting the number of multiples in a set of consecutive integers (inclusive)

A
122
Q

Average (Arithmatic mean) in a set of consecutive integers

A
123
Q

Weighted Average Equation

A
124
Q

Boundaries of a weighted average

A

The weighted average of two different data points will be closer to the data point with the greater number of observations or with the greater weighted percentage.

125
Q

Median

A

When a set of numerically ordered, the median is the value in the middle of the arranged set.

126
Q

Calculate the Median with. an Odd # of Terms

A
127
Q

Calculate the Median with. an Even # of Terms

A
128
Q

Mean = Median

A

In any evently spaced set, the mean of the set is equal to the median of the set.
EXCEPT this situation: {1, 2, 4, 5}

129
Q

Mode

A

The mode is the number that appears most frequently in a data set.

130
Q

Range of sequence

A

= Highest number in a set - Lowest number in a set

131
Q

Standard deviation range

A

High value = mean + x(sd)
Low value = mean - x(sd)

132
Q

Two important Standard Deviation rules

A
133
Q

Standard deviation = Zero

A

All data points are the same

134
Q

Avoide your fucking careless mistakes

Never tag it as mastered you idiot!

A
  1. Read carefully, word-by-word, slow down, in data sufficiency use the stem
  2. Place more focus when checking the beginning of your working!
  3. Estimate the accuracy of your final answer!
  4. Do not 🚫 get excited too soon! Double-check your work: After answering a question, go back and review your answer to make sure it makes sense and that you didn’t make any mistakes.
  5. Correctly select your final answer
  6. Within the solving:
  • Write large, neat, and clear.
  • Write out the math you’re doing on both sides of the equation every time you simplify.
  • Every time you simplify or reduce, think through exactly what you’re doing and why it works.
  • Don’t try to do too much at once. If you’re translating a word problem into math, you don’t have to translate the whole thing into a single, complex equation. It’s just as good to create two simpler equations, then combine them later.
  • Don’t miss the units.
  • One step at a time.

If your answer shows that a boy runs 2.4km in 2mins or the price of a pencil is $2000 or the bank interest rate is 80% etc, you should guess that something is off. Time to check your work again!

135
Q

Vowels

A

a, e, i, o, and u

Total 26 (5 Vowels, 21 consonants)

136
Q

Equilateral

ˌiːkwɪəlætərəl

A
137
Q

Acute triangle

əˈkjuːt

A

All angels are less than 90º

مثلث حاده

138
Q

Obtuse triangle

əbˈtuːs

A

One angle is more than 90º

مثلث منفرجه

139
Q

Quadrilateral

ˌkwɒ:drɪəˈlætərəl◂

A

چهارضلعی

140
Q

Rhombuse

A

لوزی

141
Q

Decagon

A

ده وجهی

142
Q

Unified border

A
143
Q

Data sufficiency

The length of a certain rectangular solid is 13. If the dimensions of the solid are all integers, what is its volume?

  1. The area of one of the faces of the rectangular solid is 52.
  2. The area of one of the faces of the rectangular solid is 12.
A

From statement two, we know that two of the edges of the rectangular solid must multiply together to equal 12.
This provides three different options for these two edges:

12 and 1, 6 and 2, and 3 and 4.
However, each of those options, along with the given length of 13, will give us the same volume of 156 (12 × 1 × 13 = 156, 6 × 2 × 13 = 156 and 3 × 4 × 13 = 156).
Statement two is sufficient to answer the question.

144
Q

Pentagon

penˈtægən

A
145
Q

Octagon

ˈɑːktəgɑːn

A

Octagon = 8 sides

146
Q

Minimum perimeter of a rectangle …

A

Given a rectangle with a fixed area, the rectangle with minimum perimeter is a Square

147
Q

Maximum area of a rectangle …. (with constant perimeter)

A

Given a rectangle with a fixed perimiter, the rectangle with maximum area is a square

148
Q

Area of a Hexagon with side “s”

A

Hexagon = 6 sides

149
Q

Quant
Combination

ˌkɒ:mbɪəˈneɪʃən

A

Order does Not matter

ترکیب

150
Q

The basic combination formula:

A
151
Q

Permutation

ˌpɜːrmjʊˈteɪʃən

A

Order Does matter.

جایگشت

152
Q

Basic permutation formula:

A
153
Q

Permutation formula for indistinguishable items:

A
154
Q

Number of ways to arrange a set of items in a circle:

A
155
Q

The basic probability formula:

A
156
Q

The probability of a sample space …

A

Must sum to 1.

157
Q

Probability of complementry events:

A

P(A) + P(Not A) = 1

158
Q

Probability of A and B

A
159
Q

Probability of A or B

A

Mutually exclusive: متقابلا منحصر بفرد
مثال: حیوانی که انتخاب می کنی یا سگ هست یا گربه
A and B cannot both occur
Not Exclusive: غیر منحصر بفرد
مثال: بیسکوییت برداریم یا بیسکوییت شکلاتی از بین بیسکوئیتا و آبنباتا

160
Q

Probability of choosing at least one object:

A

1 - P(none of these items occur)

161
Q

Acute angle

əˈkjuːt

A
162
Q

Right angle

A
163
Q

Straight angle

streɪt

A
164
Q

Obtuse angle

əbˈtuːs

A
165
Q

360º angle

A
166
Q

Supplementary angles

ˌsʌplɪəˈmentəri◂

A
167
Q

Exterior angle of a triangle …

A
168
Q

Parallel lines intersected by a Transversal

trænsˈvɝː.səl

A
169
Q

Area of a triangle

A
170
Q

Triangle inequality theorem

A

In any triangle, the sum of the length of two sides of a triangle is greater than the length of the third side.

  • for each triangle with a, b, and x sides, a-b < x < a+b
171
Q

Pythagorean theorem:

A
172
Q

Pythagorean triples:

A

3 - 4 - 5 Right triangle
5 - 12 - 13 Right triangle

173
Q

Isosceles Right triangle

aɪˌsɒsəliːz ˈtraɪæŋgəl

A
174
Q

The ratio of the sides of a 45-45-90 right triangle

A
175
Q

The hypotenuse of a 45-45-90 right triangle is the diagonal of a square

A
176
Q

The ratio of the sides of a 30-60-90 right triangle

A
177
Q

The Area of an equilateral triangle

A
178
Q

Cutting equilateral triangle in half

A
179
Q

The Parallelogram

ˌpærəˈleləgræm

A
180
Q

Area and Perimeter of a rectangle

A
181
Q

The longest side segment of a rectangle

A
182
Q

Perimeter and Area of a Square

A
183
Q

The Trapezoid

ˈtræpɪəzɔɪd

A
184
Q

Interior angles of a polygon …

A

The sum of the interior angles of a polygon = (n-2) x 180, where n is the number of sides in the polygon.

185
Q

Exterior angles of any polygon …

A
186
Q

Arc length and Sector Area

A
187
Q

Inscribed angle in Circles

A
188
Q

Right Triangle inscribed in a Circle

A
189
Q

Regular Polygon inscribed in a Circle

A

When a regular polygon inscribed in a circle, the polygon devides the circle into arcs of equal length.

190
Q

The Area of a Circle Ring

A
191
Q

Surface Area and Volume of a Cylinder

A
192
Q

Surface Area and Volume of a Cube

A
193
Q

Surface Area and Volume of a Rectangular Solid

A
194
Q

The Diognal of a Cube

daɪˈægənəl

A
195
Q

The Diagonal of Rectangle Solid

A
196
Q

The coordinate plane

A
197
Q

Slope of a line:

A
198
Q

The Slop-Intercept equation:

A
199
Q

Parallel lines …

A

Parallel lines have the same slope but different y-intercepts, and as a result, the lines never intersect.

200
Q

Perpendicular lines …

ˌpɜːrpənˈdɪkjʊələr◂

A

The slope of two perpendicular lines are negative reciprocals; negative reciprocals multiply to -1

201
Q

Coordinate Geometry

Distance formula:

A
202
Q

Coordinate Geometry

Midpoint formula:

A
203
Q

Functions and Sequences

Range

A

The set of all numbers a function generate (i.e. the set of all outputs) is called the range of function.

204
Q

Functions and Sequences

Domain

A

The set of all numbers a function use (i.e. the set of all inputs) is called the domain of function.

205
Q

√8

A

2.83

Iman's GMAT Quant (2 decks)

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