# Thread: SAT Math question help

1. ## SAT Math question help

When the positive integer k is divided by 7, the remainder is 6. What is the remainder when k+2 is divided by 7?

2. ## Re: SAT Math question help

Originally Posted by Mat724
When the positive integer k is divided by 7, the remainder is 6.
Can you say this using a formula? In other words, what does this phrase mean precisely?

3. ## Re: SAT Math question help

I'm sorry... I have no idea. I've tried so many times.

4. ## Re: SAT Math question help

Originally Posted by Mat724
When the positive integer k is divided by 7, the remainder is 6. What is the remainder when k+2 is divided by 7?
What is the remainder when 13 divided by 7?

What is the remainder when 15 divided by 7?

5. ## Re: SAT Math question help

how do you get 13 ans 15? im confused

6. ## Re: SAT Math question help

If m divided by n gives the quotient q and the remainder r, this means that m = qn + r and 0 <= r < n. Therefore, if m divided by n gives the remainder r, this means that for some integer q, m = qn + r and 0 <= r < n. Make sure you understand this and feel free to ask questions if you don't.

Now rewrite the phrase "When the positive integer k is divided by 7, the remainder is 6" using the pattern above and see what this says about k + 2.

7. ## Re: SAT Math question help

since its using K, i don't know what the quotient is... if K/7 has remainder 6, then K= (quotient)7 + remainder of 6.

8. ## Re: SAT Math question help

Originally Posted by Mat724
how do you get 13 ans 15? im confused
Plato gave these numbers just as examples. I think it is instructive to answer his questions.

Originally Posted by Mat724
since its using K, i don't know what the quotient is... if K/7 has remainder 6, then K= (quotient)7 + remainder of 6.
Yes, for some integer q we have k = 7q + 6. Therefore, k + 2 = 7q + 8. Can you represent this number as 7q' + r for some new q' and r such that 0 <= r < 7?

9. ## Re: SAT Math question help

When the positive integer k is divided by 7, the remainder is 6. This means that there exists number n such that $k=7n+6$ holds.
Add 2 to both sides of that equation and you get:
\begin{align*}k+2&=7n+6+2\\ k+2&=7n+8\\k+2&=7n+7+1\\ k+2&=7(n+1)+1 \end{align*}

Now you see that the remainder must be 1.