multiples

[ohjoon2]

i'm confused because my prep book is saying factors and multiples of any number MUST be positive. yet there's a sample question in my prep book that contradicts that rule.

What is the sum of the numbers in a list of m even integers?
(1) the largest integer on the list is 12
(2) the list consists of 6 consecutive multiples of 4.

the answer from the book is C because the list must be {-8,-4,0,4,8,12}.

in my head, i thought multiples must be positive since that's what i've been told.
so how is it that -8 and -4 are multiples of 4?

[kvcpk]

i'm confused because my prep book is saying factors and multiples of any number MUST be positive. yet there's a sample question in my prep book that contradicts that rule.

What is the sum of the numbers in a list of m even integers?
(1) the largest integer on the list is 12
(2) the list consists of 6 consecutive multiples of 4.

the answer from the book is C because the list must be {-8,-4,0,4,8,12}.

in my head, i thought multiples must be positive since that's what i've been told.
so how is it that -8 and -4 are multiples of 4?

It may be that you got it wrong. Factors and multiples need not always be positive.
Multiple: A number that may be divided by another number with no remainder
Factor: One of two or more quantities that divides a given quantity without a remainder. For example, 2 and 3 are factors of 6; a and b are factors of ab.

So, I would suggest you to recheck and post the exact statement that your prep material has given

Hope this helps!!

[ohjoon2]

i re-read it and it says "factors and multiples are always positive".
it also says "a multiple of x is greater than or equal to x, while a factor is less than or equal to x".
it also says "if x and y are equal to each other, each one is both a factor and a multiple of the other".

combining those rules.. using an example of an integer "20"... factors of 20 cannot be larger than 20. multiples of 20 cannot be smaller than 20. but if multiples can be negative, then it means multiples can be smaller than 20.

I'M CONFUSED!