- anonymous

When 17 is divided by k, where k is a positive integer less than 17, the remainder is 3. What is the remainder when the sum of the possible values of k is divided by 17?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6

- jamiebookeater

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- IsTim

Well, what do we know?

- anonymous

well k is less than 17 and is positive

- IsTim

Wait....ignore me...I'm...doing other stuff right now, sorry.

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## More answers

- IsTim

Someone else, please help!

- zzr0ck3r

the numbers are 7 and 14, 17/14 remainder of 3 17/(2*7) same thing
14+7 = 21
so 21/17 = 4

- zzr0ck3r

remainder of 4*

- alexwee123

lol this really sounds like a SAT 1 questions :p

- alexwee123

question*

- anonymous

it is :p

- zzr0ck3r

so the answer is 4

- helder_edwin

u r dividing 17 by k and have remainder 3 then u have the following equation
\[ \large 17=kq+3 \]

- helder_edwin

|dw:1344909696566:dw|

- helder_edwin

i'm sure u know this

- alexwee123

lol well good luck w/ the sat @lawls :p

- helder_edwin

@lawls ?

- anonymous

yeah i'm here thanks

- helder_edwin

r u following me?

- anonymous

yup

- helder_edwin

ok so since 17=kq+3 then 17-3=kq or 14=kq.
Since k is positive then q must also be positive.

- helder_edwin

what positive numbers will give u 14 when multiplied?

- anonymous

7 and 2, 1 and 14

- helder_edwin

not k=1. do u know why?

- anonymous

no why

- zzr0ck3r

17/1 = 17 with no remainder so remainder is 0 not 3

- anonymous

oh yeah i see

- helder_edwin

because you would have
\[ \large \frac{17}{1}=17 \]
and u would not have a remainder
but u r told that u DO have a remainder

- zzr0ck3r

same with 2

- anonymous

ok

- zzr0ck3r

so what do you get when you add the two choices?

- anonymous

21

- zzr0ck3r

and whats the remainder of 21/17?

- helder_edwin

correct

- anonymous

4

- helder_edwin

u got it

- anonymous

so the answer's (c) thanks guys :)

- helder_edwin

u r welcome

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