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Math Help - SAT Math question help

  1. #1
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    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?
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    Re: SAT Math question help

    Quote Originally Posted by Mat724 View Post
    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?
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  3. #3
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    Re: SAT Math question help

    I'm sorry... I have no idea. I've tried so many times.
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    Re: SAT Math question help

    Quote Originally Posted by Mat724 View Post
    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?
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  5. #5
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    Re: SAT Math question help

    how do you get 13 ans 15? im confused
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    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.
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    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.
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    Re: SAT Math question help

    Quote Originally Posted by Mat724 View Post
    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.

    Quote Originally Posted by Mat724 View Post
    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?
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    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.
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