GRE: Math Combo Flashcards
GRE Math Flashcards - Most Studied - #7,9,10,12 I deleted ones that didn't make sense ... Titles and Authors: Formulas for GRE Quantitative Section by amholt11 GRE Math by Maulleigh GRE math errors by cewind GRE Math by hsingh24 (168 cards)
0
Q
How to recognize if a # is a multiple of 12
A
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3, and 44 is a multiple of 4, so 144 is a multiple of 12.)
1
Q
Perfect Squares 1-15
A
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
2
Q
Perimeter of a rectangle
A
P= 2L + 2w
3
Q
How to recognize a multiple of 6
A
Sum of digits is a multiple of 3 and the last digit is even.
4
Q
How to recognize a # as a multiple of 4
A
The last 2 digits are a multiple of 4. (i.e 144 …. 44 is a multiple of 4, so 144 must also be a multiple of 4.)
5
Q
When dividing exponential #s with the same base, you do this to the exponents…
A
Subtract them.
i.e (5^7)/(5^3)= 5^4
6
Q
When multiplying exponential #s with the same base, you do this to the exponents…
A
Add them.
i.e. (5^7) * (5^3) = 5^10
7
Q
First 10 prime #s
A
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself
8
Q
Find distance when given time and rate
A
d=rt so r= d/t and t=d/r
9
Q
(x+y)(x-y)
A
x²-y²
10
Q
(x+y)²
A
x²+2xy+y²
11
Q
(x-y)²
A
x²-2xy+y²
12
Q
If a is inversely porportional to b, what does it equal?
A
ab=k
k is a constant
13
Q
If y is directly proportional to x, what does it equal?
A
y/x is a constant
14
Q
3 What is an important property of a 30-60-90 triangle?
A
• The ratio of the length of the three sides is x:x√3:2x
15
Q
The negative exponent x⁻ⁿ is equivalent to what?
A
1/xⁿ
i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
16
Q
2 What are the important properties of a 45-45-90 triangle?
A
• The triangle is isosceles (AC=BC).
17
Q
3 What are the important properties of a 45-45-90 triangle?
A
• The ratio of the lengths of the three sides is x:x:x√2.
18
Q
formula for distance problems
A
distance=rate×time or d=rt
19
Q
The sum of the measures of the n angles in a polygon with n sides
A
(n-2) x 180
20
Q
In any polygon, all external angles equal up to
A
360°
21
Q
In a Regular Polygon, the measure of each exterior angle
A
360/n
22
Q
The consecutive angles in a parallelogram equal
A
180°
23
Q
A quadrilateral where two diagonals bisect each other
A
Parallelogram
24
The Perimeter of a rectangle
P=2(l+w)
25
The Perimeter of a Square
P=4s (s=side)
26
Area of a Parallelogram:
A=(base)(height)
27
Distance
(rate)(time) d=rt
28
Rate
d/t (distance)/(time)
29
Time
(distance)/(rate) d/r
30
If a lamp increases from $80 to $100, what is the percent increase?
= 25%.
= (actual increase/original amount) x 100%
= 20/80 x 100% = 1/4 x 100% = 25%
31
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
32
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100%
| = 20/100x100% = 20%
33
If a>b then
-a<-b
34
If Event is impossible
P(E) = ø
35
If E is certain
P(E) = 1/1 = 1
36
Probability of Event all cases
∅≤P(E)≤1
37
Probability of E not occurring:
1 - P(E)
38
Slope
y₂-y₁/x₂-x₁
39
X is the opposite of
-X
40
The only number that is equal to its opposite
∅ ∅=∅
41
7 divided by ∅
Null
42
∅ divided by 7
∅
43
The product of odd number of negative numbers
Negative
44
∅ Is neither
Positive or Negative
45
Consecutive integers
x, x+1, x+2
46
One is (a prime or not?)
NOT A PRIME
47
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
48
∅ is a multiple of
Every number
49
2⁵/2³
2²
50
(2²)³
2⁶
51
2³×7³
(2x7)³
52
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
53
-3²
9
54
-3³
-27
55
a>b then a - b is positive or negative?
a-b is positive
56
a
a-b is negative
57
∅ is
A multiple of every integer
58
a/∅
Null
59
1ⁿ
1
60
25^(1/2) or sqrt. 25 =
5 OR -5
61
What are the real numbers?
All the numbers on the number line (negative, rational, irrational, decimal, integer). All the numbers on the GRE are real. (-2, 1, .25, 1/2, pi)
62
1/2 divided by 3/7 is the same as
1/2 times 7/3
63
10
11, 13, 17, 19
64
20
23, 29
65
30< all primes<40
31, 37
66
40 < all primes<50
41, 43, 47
67
50 < all primes< 60
53, 59
68
60 < all primes <70
61, 67
69
70 < all primes< 80
71, 73, 79
70
1/8 in percent?
12.5%
71
1/6 in percent?
16.6666%
72
3/8 in percent?
37.5%
73
5/8 in percent?
62.5%
74
7/8 in percent?
87.5%
75
5/6 in percent?
83.333%
76
x^4 + x^7 =
x^(4+7) = x^11
77
x^6 / x^3
x^(6-3) = x^3
78
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
79
a^0 =
1
80
0^0
undefined
81
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
82
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
83
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
84
Define a "monomial"
An expression with just one term (-6x, 2a^2)
85
quadratic formula
x=(-b±√(b^2-4ac))/2a
86
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
87
What is the "domain" of a function?
The set of input values for a function.
88
What is the "range" of a series of numbers?
The greatest value minus the smallest.
89
How to determine percent decrease?
(amount of decrease/original price) x 100%
90
When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
91
The larger the absolute value of the slope...
the steeper the slope.
92
What is the slope of a horizontal line?
0
93
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
94
Which quadrant is the upper right hand?
I
95
Which quandrant is the lower right hand?
IV
96
Which quadrant is the upper left hand?
II
97
Which quadrant is the lower left hand?
III
98
What are "supplementary angles?"
Two angles whose sum is 180.
99
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
100
What is a central angle?
A central angle is an angle formed by 2 radii.
101
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
102
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
103
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
104
What is a major arc?
The longest arc between points A and B on a circle's diameter.
105
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
106
What is the "solution" for a set of inequalities.
The overlapping sections.
107
What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A reflection about the origin.
108
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
109
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
110
What is the graph of f(x) shifted left c units or spaces?
f(x + c)
111
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
112
What are complementary angles?
Two angles whose sum is 90.
113
Legs 6, 8. Hypotenuse?
10
114
Legs 5, 12. Hypotenuse?
13
115
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
116
What number between 70 & 75, inclusive, has the greatest number of factors?
72
117
What are the smallest three prime numbers greater than 65?
67, 71, 73
118
Which is greater? 64^5 or 16^8
16^8
64^5 = (4^3)^5 = 4^15
16^8=(4^2)^8 = 4^16
119
5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same, what is the average of muffins per bakery sold among the remaining?
500
120
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
121
Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
9 : 25
122
Convert 0.7% to a fraction.
7 / 1000
123
Hector invested $6000. Part was invested in account with 9% simple annual interest, and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments, how much did he invest in each account?
$3,500 in the 9% and $2,500 in the 7%.
124
Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week, how many did each work?
48
125
Whats the difference between factors and multiples?
Factors are few, multiples are many.
126
How many multiples does a given number have?
Infinite.
127
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
128
If r, t, s & u are distinct, consecutive prime numbers, less than 31, which of the following could be an average of them (4, 4.25, 6, 9, 24, 22, 24)
4.25, 6, 22
129
Is 0 even or odd?
Even
130
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
131
Factor x^2 - xy + x.
x(x - y + 1)
132
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
133
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
134
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
135
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
136
(a^-1)/a^5
1/a^6
137
x^2 = 9. What is the value of x?
3, -3
138
6w^2 - w - 15 = 0
-3/2 , 5/3
139
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
140
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
141
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
142
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
143
For similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
144
What is the side length of an equilateral triangle with altitude 6?
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
145
In a triangle where the two legs are 4 and 3, what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
146
Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
147
Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
148
Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
y = (x + 5)/2
149
Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
150
What is an exterior angle?
An angle which is supplementary to an interior angle.
151
In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
152
What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
153
A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
154
A cylinder has a surface area of 22pi. If the cylinder has a height of 10, what is the radius?
1
155
What is the third quartile of the following data set: 44, 58, 63, 63, 68, 70, 82
70
156
If the 80th percentile of the measurements is 72degrees, about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
18
157
If you have a set of n objects, but you only want to order k of them, what formula do you use to determine the number of permutations?
n! / (n-k)!
158
Suppose you have a set of n objects, and you want to select k of them, but the order doesn't matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
n! / (k!)(n-k)!
159
How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 * 9 * 4)
160
There are 10 finalists for the school spelling bee. A first, second, and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
10! / (10-3)! = 720
161
There are 10 finalists for the school spelling bee. A first, second, and third place trophy will be awarded. How many different people can get the three prizes?
10! / 3!(10-3)! = 120
162
A company places a 6-symbol code on each product. The code consists of the letter T, followed by 3 numerical digits, and then 2 consonants (Y is a conson). How many codes are possible?
441000 = 1 * 10 * 10 * 10 * 21 * 21
163
Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
164
A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12, 18, and 30. What is the weight of the second brick?
2.592 kg
165
If 8 schools are in a conference, how many games are played if each team plays each other exactly once?
28. n = 8, k = 2. n! / k!(n-k)!
166
Which is greater? 27^(-4) or 9^(-8)
27^(-4)
167
Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
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