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Operations on Rational Numbers

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Jeevanantham Junior | Next Rank: 30 Posts Default Avatar
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Operations on Rational Numbers

Post Sun May 27, 2012 3:28 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If s and t are positive numbers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?
    a) 2 b) 4 c) 8 d) 20 e) 45.

    Source : OG . Please explain the way to solve this problem. What is the key point in this problem to start up solving it.

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    aneesh.kg Master | Next Rank: 500 Posts
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    Post Sun May 27, 2012 3:40 am
    Jeevanantham wrote:
    If s and t are positive numbers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?
    a) 2 b) 4 c) 8 d) 20 e) 45.

    Source : OG . Please explain the way to solve this problem. What is the key point in this problem to start up solving it.
    Let's discuss a few concepts first.

    Any number N can be represented by:
    N = Divisor*Quotient + Remainder
    Dividing LHS and RHS by Divisor,
    (N/Divisor) = Quotient + (Remainder/Divisor)
    (N/Divisor) = Integral Part + Decimal Part
    Any number when divided by another number leaves an Integral Part and a Decimal Part. The Integral Part = Quotient whereas the Decimal Part = (Remainder)/(Divisor)

    Lets return to this problem.
    Decimal Part = 0.12 = (Remainder)/t
    Remainder = 0.12t = 3t/25
    The Remainder has to be a multiple of 3 (and 't' has to be a multiple of 25).

    Among the options given, there is just one option that is a multiple of 3.
    (E) is correct.

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    Thanked by: Jeevanantham
    Jeevanantham Junior | Next Rank: 30 Posts Default Avatar
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    Post Sun May 27, 2012 3:55 am
    Thanks for your reply.

    But How come 0.12t = 3t/25 ? I did not get this point alone.

    aneesh.kg Master | Next Rank: 500 Posts
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    Post Sun May 27, 2012 4:00 am
    Jeevanantham wrote:
    Thanks for your reply.

    But How come 0.12t = 3t/25 ? I did not get this point alone.
    0.12t = 12t/100 = 3t/25
    I'm sure you could've thought of that too
    Smile

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    Jeevanantham Junior | Next Rank: 30 Posts Default Avatar
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    Post Sun May 27, 2012 4:02 am
    Yup... Smile You made it simple... Thanks man..

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