Quant Flashcards
Sum of 3 numbers = 3 times one of numbers
Median = average of 3 numbers
The number that is x3 is the average/median.
Prime to an exponent
Factor the product into a prime box
Find average equation
Sum of terms/number of terms
Given right triangle hypotenuse and area
Sufficient to find perimeter. Substitute pythag theorem with area.
Vertex located on midpoint of larger triangle
Smaller triangle area is 1/4 that of the larger. 1/2 base size and 1/2 height size
30-60-90 Triangle angle to side relationships
Opposite of:
30 - x
60 - x(sqrt(3))
90 - 2x
Probability of x AND y
Multiply probability
Probability of x OR y
Add probability
First (11) prime numbers
2,3,5,7,11,13,17,19,23,29,31
Terms need to be in alphabetical order
Can be AB, AC, AD, not just AB, BC, CD, etc.
Rate - time - distance (approach)
Set up a RxT = D chart
Sum of consecutive integers formula
S = (1st + last)/2 * (Last - first + 1)
Arranging digits in a required pattern (approach)
Draw examples of each pattern/possible choice
ie: DS209
Finding min answer
use extremes for smart numbers or test cases
(x+y)^2
x^2 + 2xy + y^2
(x-y)^2
x^2 - 2xy + y^2
(x-y)(x+y)
x^2 - y^2
A system of inequalities (approach)
Stack them and add
(2) inequality signs in a statement
Split them and solve separately
First step in inequ equation
Try algebra
Then test numbers
If x is doubled, then y is tripled (or similar statement) (Approach)
Test cases
One variable in the question stem (ie: s^3 + 12 =?)
Isolate the q stem to one variable (ie: what is s?)
What is volume? (Approach)
Draw the picture and get the equations on paper
A trianglein a semi circle (hyp is the diameter)
Triangle is a right triangle
Looking for whether a combination of variables are odd/even
List out each variable and determine if it is odd even or either
Small % and smart numbers (ie: 4.5%)
use 1000 to account for 0.5% in avoiding decimals in answers
% of two different variables in comparison to a % of the sum
Weighted averages
Partial list in question
Draw list on page and fill out as you go
Working backwards to find the min value
Start with the smallest answer choice
Main number properties to try in testing cases
Pos/Neg; Odd/Even; Fraction/Int; Zer0
Comparing fractions (esp in intervals)
Put into common denominator on paper
% Increase/decrease (algebra)
(1+ x/100) or (1- x/100)
Finding greatest value in overlapping set
Put > or < in matrix
Relationship between 3 sides of a triangle
Third side must lie between the difference and the sum of the other 2
3 most common triangles
30-60-90
45-45-90
3-4-5
Diagonal of a rectangle (approach)
Use pythagorean theorem with sides
Diagonal of a cube
x√3
(2) rules for similar triangles
- ) Sides are directly proportional
2. ) Angles are the same
Compare the areas of similar triangles
- Given sides a:b
- Area is a^2 : b^2
Maximize the area when given 2 sides of a triangle
Make 2 sides perpendicular to each other / right triangle
Sum of angles of any polygon (n sides)
(n-2)(180)
Area of trapezoid
( (B1 + B2) (h) ) / 2
Area of parallelogram
(b)(h)
Area of rhombus
(Diagonal 1 x Diagonal 2) / 2
Relationship between a central angle and the arc it intercepts
Proportion of central angle to 360 : proportion of arc length to center of circle
Relationship between central angle and inscribed angle
Inscribed is 1/2 of central angle
Surface area of a cylinder
2πrh + 2(πr^2)
Quadrants
I - IV, counterclockwise from top right
DS Process
- Deep breath
- Identify givens
- Yes/no v. val
- Answer grid
- Rephrase question
- Prove statement to be S or NS
PS Process
- Deep breath
- Glance at answers
- Read question
- Jot givens
- Reflect on strategy
- Organize/work
Working backwards when given that x is greater than y
Eliminate answers when working backwards where y is greater than x
Working backwards when given that x is greater than y
Eliminate answers when working backwards where y is greater than x
Variables in answer choice
Smart numbers if algebra doesn’t look easy
Finding % complete of a combined rate
Make a new RxT=D chart
Find slope greater or less than 1
Wrtie rise/run for slope
Discount or markup between 1-100
Test max/min cases within parameter
Unknown multiplier with modifications including real numbers (building block ex)
Adjust fractions with modifiers and solve for x (or multiplier)
Dollars and cents for smart numbers. how to choose smart nubers (taxi rate example)
Double or dingle digit number for dollars
Triple digit for cents
Dollars and cents in the question stem to be used in an equation (approach) (taxi rate example)
Assign smart numbers but convert to dollars before solving
Consecutive set with odd number of terms
sum of integers is a multiple of the number of terms
Consecutive set with even number of terms
Sum of integers is not a multiple of the number of terms
“X is the sum of Y consecutive terms” What does Y represent?
The number of consecutive terms in the set
% for quantity of something before and after a modification (gold/silver example)
Write as a fraction with total in denominator
Probability of something happening, often in a series of events (technique?)
Use the (1-x) technique. Where you find the opposite event and subtract it from 1.
Probability of a sequence of events (how to capture on paper)
Use a table to show each step
x^2 - y^2 = a given int
Can solve for x and y by listing the squares of integers and comparing differences
Rhombus definition
Parallelogram with (4) even sides
Find minimum of a set of numbers
Maximize every other number in the set
A decimal raised to an exponent (simplify)
change the decimal to a fraction if possible
Any 3 numbers in a set = a given int
All numbers in the set are the same
Sum of angles of polygon
(n-2)(180)
Intersecting lines with angles
Opposite angles are equal
Adjacent angles sum to 180
Write it on the paper
Multiply a number by 10
Each digit moves “up” one place
Multiple equations that share a point (r,s)
Plug the point in and solve for the system of equations
A number raised to a larger exponent (eg (33)^43 and (43)^33)
Find patter in 3^2, 3^3, 3^4, etc.
Sum of consecutive set
Find the average (1st + last)/2 times the # of terms
Find a % of a big complex number (approach)
First find 10% of the number then add and subtract increments of 5% or 1% to hone in on the desired percent
14^2
196
15^2
225
16^2
256
17^2
289
Approximate (approach)
Estimate/round number whenever possible
Find number of options when order is not important
Multiply the number of options in each position of the sequence together for the total number possible
(3) equations that share a point on a coordinate graph
Plug the point into the system of equations and solve
Expression divided by 2 with solution that must be integer
Look for even terms
Arc length (approach)
Start with circumference as proportion of central angle
Probability of favorable outcome (approach)
Use anagram method for favorable outcomes over total number of outcomes for probability
Int^x (ex: 12^x) simplify
Split out factors and raise to x (ex: 2^x * 3^x)
Volume ratio with no real # (approach)
- ) ID smart # for volume
- ) ID target value
- ) Work backwards from answers
Small group size for probability
Write out every option
Factor a large number into a prime tree when looking for multiples (what to watch out for)
Can combine primes to make different factors of the larger value
Average of consecutive set
Last term + 1st term divided by 2
Time interval question (approach)
Run through the problem, increasing the interval each step to get different values
