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GRE Quantitative Study Guide
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Terms in this set (122)
What are digits?
Numbers the make up other numbers
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
What are integers?
Counting numbers
Are fractions integers?
No
Can integers be even or odd?
Yes
Is zero positive or negative
It's neither
Is zero even or odd?
Even
Can you divide a number by 0?
No
What are consecutive integers?
Numbers listed in order (increasing or decreasing). Can count by 1s, 2, 3s, etc.
What is the absolute value of a number equal to?
The number's distance away from) on the number line.
Can the absolute value of a number be negative?
No, it's always positive.
|-5| = 5 and |5| = 5
How many factors does a prime number have?
Only 2 factors, 1 and itself
Are 0 and 1 prime numbers?
No
Are there any even prime numbers?
Yes, the number 2
Can negative numbers be prime?
No, prime numbers are only positive
What is the quotient?
The result of division
What is the product?
The result of multiplication
What are the orders of operation?
PEMDAS
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
Distributive Property: a(b+c) is the same as...
ab + ac
Distributive Property: a(b-c) is the same as...
ab - ac
Exponent Rule: a2 is the same as...
a x a
Exponent Rule: a2·a3 is the same as...
a2+3 = a5
Exponent Rule: (a2)3 is the same as...
a2·3 = a6
Exponent and Cube Root Rule:
3√a12 = (a12)1/3 = a 12/1 x 1/3 = a12/3 = a4
Exponent Rule: a6/a2 is the same as...
a6-2 = a4
A number raised to the first power (10001) is always _________.
The number itself (10001 = 1000)
What is 00?
Undefined
What is a number raised to the power 0 (10000)?
1 no matter what the number is
(10000 = 1)
What happens to a number raised to a negative power? 2-2
It becomes 1 over the number raised to a positive power
(2-2 = 1/22 = 1/4)
Does a negative number raised to an odd power become negative or positive? (-23)
It stays negative
-23 = -8
Does a negative number raised to an even power become negative or positive? (-22)
It becomes positive
-22 = 4
If you raise a fraction between 0 and 1 to a power greater than 1 will the number become larger or smaller?
Smaller
(1/2)2 = 1/4
If you raise a number other than 1 to a power greater than 1 with the number become larger or smaller
Larger. 22 = 4
Can you simplify 274?
3x3x3=27, so (3x3x3)4 which equals (3x3x3)(3x3x3)(3x3x3)(3x3x3), so 312
How do you divide and multiply square roots?
Just like any other number
√3 x √12 = √36
√16 = √16 = 4 = 2
4 √4 2
Can you add or subtract square roots?
Only if the roots are equal
√2 + √2 = 2√2 (same root = 1√2 + 1√2)
but √2 + √3 ≠ √5
Estimate √32
√32 is in between √25 and √36, so we can guess that √32 is somewhere between 5 and 6
Simplify √32
32 has a factor that is a perfect square, 16, so √32 = √16x2 = 4√2
What is the absolute value of √a2
√a2 = |a| for all value of a
What is √1
1
What is √2
1.4
What is √3
1.7
What is √4
2
If ETS asks for the value of √16, do they want a positive or negative root?
They only want the positive root.
Is x2=16 the same as √16?
No because in x2 = 16, x = ±4,
but √16 = +4 (NOT -4)
What is foil?
First, Outer, Inner, Last
(x + 4)(x + 3)
(x · x) + (x · 3) + (x · 4) + (4 · 3)
x2 + 3x + 4x + 12
x2 + 7x + 12
What is the unfactored form
of x2 - y2
(x+y)(x-y)
What is the unfactored form of
(x+y)2
x2 + 2xy + y2
What is the unfactored form of
(x-y)2
x2 - 2xy + y2
What is the factored form of
(x+y)(x-y)
x2 - y2
What is the factored form of
x2 + 2xy + y2
(x+y)2
What is the factored form of
x2 - 2xy + y2
(x-y)2
Inequalities (ie: 12-6x>0)
What happens to the inequality symbol when you multiply and divide?
12 - 6x > 0
-12 -12 (+/- no change in direction)
-6x > -12
-6x -6x (x/div. change direction)
x < 2
When can you plug-in?
When there are variables in the answer choices
How do you know when you can plug in the answer?
(ie: plug-in one of the given answers)
1. When the question begins with: How much..., How many..., What is the value of...
2. Answer choices are in ascending or descending order
3. Your tempted to make an algebraic equation
When plugging in the answer, what answer should you assume is correct?
C. Use C as a starting point
In Quantitative Comparison questions, how many times should you plug-in?
Always plug-in at least twice
When you plug-in for a Quantitative Comparison, what should you start with?
Something nice and happy
When you plug-in for a Quantitative Comparison, what should you plug in the second time?
Use ZONE F
What is ZONE F
Zero
One
Negative
Extremely small or big
Fractions
Percentages
How do you set-up:
1. 5 is r percent of 25
2. s is 25 percent of 60
r
1. 5 = 100 (25)
25
2. s = 100 (60)
Percentage Increase/Decrease Formula
Difference
Percentage Change = original x 100
What is the original number in a percentage INCREASE problem?
The smaller number
What is the original number in a percentage DECREASE problem?
The larger number
What is the difference in a percentage increase/decrease problem?
The larger number minus the smaller number
Can you plug-in for fraction and percentage problems?
Yes. Plugging in for the missing value will make your life much easier!
What is a Ratio?
A ratio expresses relationships in part to part
What is the key to dealing with ratio questions?
Finding the whole or the total
A ratio of 2:1 has how many total parts?
3
How do you figure out what number to multiply by?
You take the total number of coins (24) and divide it by the total of the ration (2:1 = 3), so 24 divide by 3 = 8. Then you multiply each item (pennies and nickels) by 8 to figure out the total number of each coin in the pocket.
What are proportions?
The equivalent relationship between two fractions or ratios
What is the formula for finding the Average?
Total
Average = # of things
What is the mean?
The average
Add all the numbers and divide the total by the number of numbers.
ie: 5, 1, 4, 6 = 16/4 = 4 is the average
What is the median?
The middle value in a set of numbers
In the set {1,2,3,4,5,6,7), the median is 4
In the set {1,2,3,4,5,6), the median is the average of 3+4/2 (3.5)
What is the mode?
They number in a set that occurs the most frequently
What is the range
The difference between the biggest and smallest number in the set.
In the set {2, 6, 13, 3, 15, 4, 9}, 15 is the biggest and 2 is the smallest, so 15-2 = 13 (the range)
What is the formula to find the time in a rate problem?
t = d/r
What is the formula to find the distance or amount in a rate problem?
d = rt
Can standard deviation ever be negative?
No, standard deviation can only be positive.
So if you see negative numbers in a standard deviation quantitative comparison question, chances are the answer is D (cannot be determined)
Will ETS make you calculate standard deviation?
No, so if ETS is asking for you to calculate standard deviation, then chances are the answer is D (cannot be determined)
Is a line an angle?
Yes, it is a perfectly flat angle of 180°
How many angles are formed when 2 lines intersect?
Four angles
What is the sum of the angles when 2 lines intersect?
360°
How many degrees do the three angles inside a triangle equal?
180°
What is an equilateral triangle?
All three sides are equal in length
Each angle is 60°
What is an isosceles triangle?
Two sides are equal in length
Two angles are equal
How do you find the perimeter of a triangle?
The sum of all three sides
What is the third side rule?
The length of any one side of a triangle must be less than the sum of the other 2 sides and greater than the difference between the other 2 sides. So if a triangle as 2 sides, 3 and 5, then 3 + 5 = 8 and 5 - 3 = 2. Therefore, the third side must be between 2 and 8.
How do you find the area of a triangle?
A = ½ bh
For what type of triangles can you use the Pythagorean Theorem?
Only right triangles
What is the hypotenuse?
The side of the triangle opposite the right angle or the longest side.
What is the Pythagorean Theorem?
a2 + b2 = c2 * c = hypotenuse
What are the most common right triangles?
(3, 4, 5), (6, 8, 10), and (5, 12, 13)
How do you create a right isosceles triangle?
By cutting a square in half.
What is the ratio of sides in a right isosceles triangle?
x : x : x√2
A 30:60:90 triangle is what type of triangle cut in half?
An equilateral triangle
What is the ratio of sides on a 30:60:90 triangle?
x : x√3 : 2x
How do you find the perimeter of a four-sides object?
The sum of the lengths of all the sides
How do you find the area of a rectangle or square?
A = length x width
What is the radius of a circle?
The line from the center to the side
What is the diameter?
The line from one side to the other that goes through the center or 2 times the radius (r)
D = 2r
How do you calculate the circumference of a circle?
2πr or πd
How do you find the area of a circle?
Area = πr2
What is the equation of a line?
y = mx + b
m= the slope
b = y-intercept
How do you find b in the equation of the line?
b is where the line crosses the y-axis
What is the formula for finding m, the slope of a line?
y2 - y1
m = x2 - x1
How do you find the volume of a rectangle?
Length x width x height
How do you find the volume of a cylinder?
Find the area of the circle and multiply that by the height. πr2 x height
How do you find the surface area of a rectangle?
Sum of the area of all of its sides
What is probability?
# of possible outcomes that satisfy the condition
# of total possible outcomes
If you have 10 shirts and 3 of them are black, what is the probability of selecting a black shirt from the closet without looking?
3/10 (3 out of 10)
How do you find the probability of a series of events in a row?
The probability of A and B.
A and B = probability of A x probability of B
How do you find the probability of either one event or another?
The probability of selecting A or B.
A or B = probability of A + probability of B
How do you find the probability of an event not happening?
Given event A,
A + not A = 1
What is the factorial of a number?
ie: the factorial for 6!
The number times every positive whole number smaller than that number down to 1
ie: 6! = 6x5x4x3x2x1 = 720
What is a permutation?
An arrangement of things in a particular order
ie: how many different ways can you arrange 5 statues on a shelf?
5x4x3x2x1 = 120 different ways
How do you solve a permutation?
•Figure out how many slots you have
•Write down the number options for each
•Multiply them
How do you know if it is a permutation problem?
Permutation problems usually ask for:
•Arrangements
•Orders
•Schedules
•Lists
Solve: Five people are running in a race. The winner will get a gold medal, the person who comes in second will get a silver medal, and the person who comes in third will get a bronze medal. How many different orders of gold-silver-bronze winners can there be? How many slots, how many options?
Is it a permutation or combination? Permutation because it asks for the order.
There are 5 people and three possible prizes so,
Slots = 3 (possible prizes)
# of options = 5 people (slot 1), 4(slot 2), 3 (slot 1)
so 5x4x3 = 60 different orders
What is a combination?
A group where the order of elements within the group doesn't matter.
How do you know if it is a combination problem?
Permutation problems usually ask for:
•Groups
•Teams
•Committees
How do you solve a permutation problem?
•Figure out how many slots you have
•Write down the number options for each
•Divide by the factorial of the number of slots
Solve: A pizza can be ordered with any of eight possible toppings. How many different ways can you order a pizza with three different toppings?
"any of eight possible toppings" = group in no particular order, so this is a combination problem
Slots = 3 different toppings
# of options = 8 possible toppings
so 8x7x6 (possible topping in 3 slots)
3x2x1 (factorial of the number of slots)
= 56 different ways
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