GRE Prep

True/False: is zero NOT an integer

False, it is an integer

True/False: Every integer has a negative counterpart

False, 0 does not have a negative (everything else does)

is infinity an integer?

no

what do you get: a negative times a negative

always positive

what do you get: negative number added to a negative

always negative

what can you get: a negative number subtracted from a negative

can be negative, 0, or positive

what do you get: a negative number divided by a negative

always positive

what do you get: a negative number raised to a positive

can be positive or negative

what do you get: a negative raised to a negative

can get positive or negative

inclusive integer rule (how many integers are there from # to #)

Last - First +1

1 and itself is…

always factors/divisors

nifty finding factor system

start with 1 and #, make gap smaller

how to find the sum of integers in intervals for even

write out first 3 and last 3 to find what the pair sum is, divide by 2, multiply # of pairs by that sum

how to find sum of integers in intervals for odd

write out first 3 and last 3 to find what pair sum is, subtract last number by 1 and divide by 2, whatever that number is subtract by last and add it to first to see what that middle number is, then multiply # of pairs by that sum and then add the middle number

divisibility rules: how to know if 2 is a factor

if the integer ends in 0, 2, 4, or 8

divisibility rule: how to know if 3 is a factor

sum of digits of integer, then look to see if 3 divides evenly into it

divisibility rules: how to know if 4 is a factor

look at last two digits, see if it’s divisible by 4

even ± even =

even

even ± odd =

odd

odd ± odd =

odd

even x even =

even

even x odd =

even

odd x odd =

odd

even / even =

both or neither

even / odd =

even or neither

odd / odd =

odd or neither

even ^ integer =

even except when integer is 0 (even ^0 = 1)

odd ^ integer =

odd

divisibility rule: is it a factor of 5

look at last number, if it is a 0 or 5

divisibility rule: is it a factor of 6

6 is 2×3 so see if it passes both the 2 and the 3 rule

divisibility rule: is it a factor of 8

look at the last 3 digits of number

divisibility rule: is it a factor of 9

same as 3 Rule, add digits of integer and see if 9 can divide into it cleanly

True/False: every integer with a 0 at the end is divisible by 10

True: multiples of 10 end in 0

True/False: Every integer that is divisible by 22 and 33 is divisible by 66

True: as long as that integer can be divided by both 22 and 33, it can be divided by 66.

True/False: Every even integer divisible by 5 is also divisible by 10

The third option would be true since 10=2×5, so you need both a 2 and a 5 to be divisible by 10. Every even integer has a 2

divisibility of 11 rule

do a + then - pattern for each number then combine those values. if it’s a multiple of 11 then it’s divisible

1 is a (multiple/factor) of every integer

factor

0 is a (multiple/factor) or every integer

multiple