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Can you help with this problem? Thanks!

This topic has 1 expert reply and 2 member replies
yumi2012 Senior | Next Rank: 100 Posts
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Can you help with this problem? Thanks!

Post Tue Sep 03, 2013 7:07 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If s and t are positive integers 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

    Diagnostic Test
    Question: 13
    Page: 22
    Difficulty: 650

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    ganeshrkamath Master | Next Rank: 500 Posts
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    Post Tue Sep 03, 2013 8:03 pm
    yumi2012 wrote:
    If s and t are positive integers 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

    Diagnostic Test
    Question: 13
    Page: 22
    Difficulty: 650
    s/t = 64.12
    s = 64t + 0.12t
    0.12t = 3*4/100 * t
    = 3/25 * t

    For 0.12t to be an integer, t should be 25,50,75,100,...
    So 0.12t = 3,6,9,12,....
    So the remainder 0.12t is always a multiple of 3.

    Choose E

    Cheers

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    http://www.beatthegmat.com/first-attempt-750-in-2-months-t268332.html#688494

    Post Tue Sep 03, 2013 8:42 pm
    Quote:
    If s and t are positive integers 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
    When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
    There is a relationship between the two representations:

    Remainder/Divisor = Decimal.

    When 5 is divided by 2:
    Remainder representation: 5/2 = 2 R1.
    Decimal representations: 5/2 = 2.5.
    Remainder/Divisor = 1/2.
    Decimal = .5.
    Since the two values are equal:
    Remainder/divisor = decimal.

    We should write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

    In the problem above:
    Remainder = R
    Divisor = t
    Decimal = .12 = 12/100 = 3/25.
    Plugging these values into remainder/divisor = decimal, we get:
    R/t = 3/25.

    Since R/t is in its most reduced form, we know that t must be a multiple of 25 and that R must be a multiple of 3.
    Only answer choice E is a multiple of 3.

    The correct answer is E.

    Similar problems:
    http://www.beatthegmat.com/quotient-remainder-problem-t101371.html
    http://www.beatthegmat.com/remainder-t176105.html

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    Java_85 Master | Next Rank: 500 Posts
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    Post Tue Sep 03, 2013 8:50 pm
    Nice question!

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