Quant Flashcards by Matt Anderson

Sum of 3 numbers = 3 times one of numbers

Median = average of 3 numbers

The number that is x3 is the average/median.

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Prime to an exponent

Factor the product into a prime box

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Find average equation

Sum of terms/number of terms

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Given right triangle hypotenuse and area

Sufficient to find perimeter. Substitute pythag theorem with area.

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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

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30-60-90 Triangle angle to side relationships

Opposite of:
30 - x
60 - x(sqrt(3))
90 - 2x

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Probability of x AND y

Multiply probability

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Probability of x OR y

Add probability

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First (11) prime numbers

2,3,5,7,11,13,17,19,23,29,31

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Terms need to be in alphabetical order

Can be AB, AC, AD, not just AB, BC, CD, etc.

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Rate - time - distance (approach)

Set up a RxT = D chart

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Sum of consecutive integers formula

S = (1st + last)/2 * (Last - first + 1)

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Arranging digits in a required pattern (approach)

Draw examples of each pattern/possible choice

ie: DS209

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Finding min answer

use extremes for smart numbers or test cases

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(x+y)^2

x^2 + 2xy + y^2

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(x-y)^2

x^2 - 2xy + y^2

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(x-y)(x+y)

x^2 - y^2

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A system of inequalities (approach)

Stack them and add

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(2) inequality signs in a statement

Split them and solve separately

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First step in inequ equation

Try algebra

Then test numbers

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If x is doubled, then y is tripled (or similar statement) (Approach)

Test cases

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One variable in the question stem (ie: s^3 + 12 =?)

Isolate the q stem to one variable (ie: what is s?)

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What is volume? (Approach)

Draw the picture and get the equations on paper

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A trianglein a semi circle (hyp is the diameter)

Triangle is a right triangle

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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

1. ) 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

1. Deep breath 2. Identify givens 3. Yes/no v. val 4. Answer grid 5. Rephrase question 6. Prove statement to be S or NS

PS Process

1. Deep breath 2. Glance at answers 3. Read question 4. Jot givens 5. Reflect on strategy 6. 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)

1. ) ID smart # for volume 2. ) ID target value 3. ) 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