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Thread: Help with a little arithmetic problem

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    Help with a little arithmetic problem

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    Hello, this silly problem has me wondering.... help! Can someone explain please? Thank you!

    When the positive integer n is devided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n?

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    An Urch Guru Pundit Swami Sage
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    Re: Help with a little arithmetic problem

    quickly playing with numbers gets me to say 11 and that is probably the best way to solve this.

    We know that n-2 is divisible by 3 and n-1 is divisible by 5. So just look at numbers that end in 6 and 1 (n-1 is divisible by 5) and find one where n-2 is also divisible by 3. The first one you get is 11.

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    Re: Help with a little arithmetic problem

    Quote Originally Posted by YaSvoboden View Post
    quickly playing with numbers gets me to say 11 and that is probably the best way to solve this.

    We know that n-2 is divisible by 3 and n-1 is divisible by 5. So just look at numbers that end in 6 and 1 (n-1 is divisible by 5) and find one where n-2 is also divisible by 3. The first one you get is 11.
    That's the correct answer! Thank you!

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    GRE-GMAT Instructor Brent Hanneson's Avatar
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    Re: Help with a little arithmetic problem

    When it comes to remainders, we have a nice rule that says:

    If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
    For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

    When the positive integer n is divided by 3, the remainder is 2

    So, some possible values of n are: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29,....etc

    When n is divided by 5, the remainder is 1.
    So, some possible values of n are: 1, 6, 11, 16, 21, 26, 31 .... etc

    We can see that 11 is the smallest number that BOTH lists share

    For more info on remainders, see our free video: GRE Integer Properties | Greenlight Test Prep

    Cheers,
    Brent

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