Quant Flashcards by Katy Svennas

2 equations 2 unknowns

Can be solved (sim eqn if needed) to give the variables IF they are different (ie must check it’s not just the same equation simplified)

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x^(n-1) > x^(n); eg. x > x^2 (i.e. raising to larger exponent gives smaller number)

0< x <1 (x is a fraction) OR x is a negative number and n is an odd number

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exponents

to which base?

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Population problem (growth)

Population chart

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Comparing inequalities with a variable

Draw it out on number line; don’t multiply or divide by variable UNLESS sign is known!

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Inequalities

DRAW NUBMER LINE! Might need to use modulus to make sense of it

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Two separate inequalities

Can I line them up or add them up? (add only if direction is same; also NEVER subtract or divide)

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Inequalities that can’t be summed or other method

Test cases: with a positive and negative integer, and a positive and negative fraction!

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Absolute value equation with variable on both sides

Set equal to plus/minus AND check final answers work by plugging back in (find that usually only one does)

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Expression in absolute value signs

Can expression actually be negative? If with an x^2 maybe not!

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sqrt(x^2)

modulus(x)

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Modulus linear eqn

DRAW NUBMER LINE! Might need to use modulus to make sense of it

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A quadratic in a DS problem

Can one of the solutions be eliminated based on some contraint in the problem? Or are the two solutions the same? Or give the same answer

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A sequence that is not arithmetic or consecutive

Write it out, don’t try and come up with a formula!

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what is the units digit

Last digit shortcut: only pay attention to units digit (for multiply and plus only)

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terminating decimal

Put in form of: some integer/some power of 10; if after being fully reduced has any prime factors besides 2 or 5, will not terminate!

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Compare fractions; which is bigger?

Cross-multiply (don’t bother finding LCD)

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Fraction question with fractions in the answers

Use smart numbers

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x = -y

Same absolute value; 0 is halfway between on number line

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Is a divisible by b?

Prime Factorization! Break a and b down into their primes, a MUST be divisible by the primes of b (USE DIVISIBILITY RULES!). Faster than long division

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ab/c

Either a or b or both is divisble by c

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asking whether a number with a high power is divisible by another (meaning it would take a long time to find the number)

Factorise and break into primes

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a is a divisor of b; b is divisible by a

Prime factorization; b = an (where n is a positive integer); b > a; odd or even?

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a is a factor of b

Prime factorization; b = an (where n is a positive integer); b > a

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b is a a multiple of a

Prime factorization; b = an (where n is a positive integer); b \> a

Prime number question

Is number odd or even? Cannot be even and \>2

Remainder; eg. a has a remainder of c when divided by b

a - c = bn: aka subtract remainder then will be divisible by b

Remainder; eg. a has a remainder of c when divided by b

Manipulate expression to put in terms of what you know is divisible by b: since if N is a divisor of x and y, then N is a divisor of x +/- y

2n + 1

Odd number

Divisible by 2

Even number

Odd number being divided by another number or that is the product of other numbers that are stated as odd or even

Turn into multiplication form: odd number can only result from odd x odd; otherwise doesn't result in integer

Problem asking if expression is odd or even in DS

Test cases with x = odd and x = even! Then can probably rephrase as x being odd or even will make expression either odd or even

Expression \> 0 or \< 0

Positives and negatives question! Make a table and test cases with each combination of + and - for the variables (don't forget to test for = 0 too!)

The factors of a variable instead of a number

PARTIAL prime box, only take overlapping factors as others might be redundant

7, 5, 3, 2 in a question

Prime Factorization!

b/a results in a positive integer

a is a factor of b

A quadratic in a DS problem

Can one of the solutions be eliminated based on some contraint in the problem? Or are the two solutions the same? Or give the same answer

A sequence that is not arithmetic or consecutive

Write it out, don't try and come up with a formula!

what is the units digit

Last digit shortcut: only pay attention to units digit (for x and + only)

terminating decimal

Put in form of: some integer/some power of 10; if after being fully reduced has any prime factors besides 2 or 5 _ will not terminate!

Compare fractions - which is bigger?

Cross-multiply (don't bother finding LCD)

Fraction question with fractions in the answers

Use smart numbers

Ratio Q that has real value (ground the ratio to real values)

Find the unknown multiplier to find the actual values

Two types of things, whose relationship to one another changes and is only given in RELATIVE VALUES

RATIOS! Relative values are just ratios in disguise

several correct possible answer in a PS problem

Is there an integer constraint?

Integer or other constraints bc objects or people, esp on DS

FIRST thought should be: TEST CASES! Then check if algebra works Esp wth variable in exponent

Need to do long division or long multiplication

Break down into prime factors and match (two equal numbers MUST have same number of prime factors)

points on a coordinate system

Draw out the picture - use logic if algebra doesn't work

Find the area of a triangle/polygon that is not straightfoward to find using standard formula, but is circumscribed in another shape

Is it easier to find area by subtracting overall shape by smaller shapes surrounding desired area?

Triangle with sides 3-4-5 or other known triples

Triangle must be a right triangle

A small triangle and a big triangle

Are they similar? Check for matching angles

Special triangle (3-4-5; 45-45-90 etc)

LABEL all additional information that can be found from known relationships

Square and diagonal

Special triangle 45-45-90: can find diagonal with side and vice versa

If there is a triangle inscribed in a circle with a right angle

Hypotenus must be the diameter of the circle

(n-1)n(n+1) OR JUST (n+1)(n+2)(n+3)

Consecutive integers! Exactly one term in the set of k integers will be divisible by k

x is the sum of 5 consecutive numbers

x + x + 1 + x +2 + x + 3 +...; even number = sum is not a multiple of number of terms; odd number = sum is multiple of number of terms

A words problem with percents as variables

Use smart numbers; easier to grasp with concrete numbers

Find the average time for a given distance

Put two times in terms of distance and speed; for fxed distance: ratio of speed = inverse of ratio of time

List of numbers with two variables, and the median

Test cases to see where the variables can be placed to give median

mixture problem (eg. 20percent of A and 50percent of B give 80percent of the total (A+B)

find ratio of two elements

Sum of consecutive integers

if n = even: sum is NOT a multiple of n if n = odd: sum IS a multiple of n

product of consecutive integers

is divisble by k! Will constain EXACLTY ONE multiple of k

equilateral triangle

30-60-90 triangle height = sqrt(3)/2 \* side

If N is a divisor of x and N is a divisor of y

N is a divisor of x + y See how to manipulate equation to be in terms of what you know is divisble by the number: makes it into an expression, then maybe separated term is also divisible by that number so whole expression is divisible by that number

sum of two primes is odd

one of primes must be 2

sum of two primes, neither of which is 2

must be even