quant - magoosh Flashcards
what is standard deviation?
standard deviation is a quantification of data points in a set relative to the mean
a wider spread of values leads to a ______ standard deviation
higher
extremes values far from a mean ______ deviation
increase
values closer to a mean _______ standard deviation
decrease
what’s the connection between the distance & work formulas?
they have the same format.
(rate)(time) = result (distance/work)
outline the division formula
dividend = (divisor)(quotient) + remainder
even integer x odd integer =
even integer
even integer ÷ odd integer =
even integer
even integer^[2(odd integer)+1] =
odd integer — multiplying an odd integer leads to another even integer, but a +1 has been added, making it odd
even integer^[odd integer] =
even integer
odd integer ÷ even integer =
not an integer. because they are odd numbers, they are not divisible by 2, leading the quotient to becoming a fraction.
for a set of consecutive, positive integers that are evenly spaced, the mean and median are…
equal. the sum of the integers are symmetrically distributed around the median
squaring multiples of 10 rule
- square digits without the zero
- add on two zeros at the end
example: 30² —> 3² —> (9)(10²) = 900
squaring any number ending in 5 always ends in…
25
any number ending in 5 is halfway between two multiples of…
10
squaring multiples of 5
- isolate other digits from 5
- add one to the remaining digit
- multiply those digits together
- put the product of those numbers in front of 25 (5 squared)
example: 75²
7
7 + 1 = 8
(7)(8) = 56
5625
squaring adjacent numbers formula
one digit up: n² + n + (n + 1) = (n + 1)²
one digit down: n² - n - (n - 1) = (n - 1)²
percentage change formula
(change ÷ original) x (100%)
work / rate / time formula
work done = (rate)(time)
doubling & halving rule
- in any multiplication, doubling one factor & halving the other will keep the same product
- numbers should be made into a multiple of 10 to simplify the calculation
example:
(16)(35) = (8)(2)(35) = (8)(70) = 560
when is the doubling & halving rule most helpful?
- when one factor ends in 5
- when one factor is an odd multiple of 50
