Quant Flashcards
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)
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
exponents
to which base?
Population problem (growth)
Population chart
Comparing inequalities with a variable
Draw it out on number line; don’t multiply or divide by variable UNLESS sign is known!
Inequalities
DRAW NUBMER LINE! Might need to use modulus to make sense of it
Two separate inequalities
Can I line them up or add them up? (add only if direction is same; also NEVER subtract or divide)
Inequalities that can’t be summed or other method
Test cases: with a positive and negative integer, and a positive and negative fraction!
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)
Expression in absolute value signs
Can expression actually be negative? If with an x^2 maybe not!
sqrt(x^2)
modulus(x)
Modulus linear eqn
DRAW NUBMER LINE! Might need to use modulus to make sense of it
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 multiply and plus 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
x = -y
Same absolute value; 0 is halfway between on number line
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
ab/c
Either a or b or both is divisble by c
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
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?
a is a factor of b
Prime factorization; b = an (where n is a positive integer); b > a
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
