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Remainders Question - Nova

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shanice Really wants to Beat The GMAT! Default Avatar
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Remainders Question - Nova Post Wed Apr 11, 2012 6:02 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    1) The remainder when positive integer m is divided by n is r. What is the remainder when 2m id divided by 2n?

    a)r b)2r c)2n d)m-nr e)2(m-nr)

    Answer is B.

    Explanation:
    Since the remainder when m is divided by n is r, we can represent m as m = kn + r, where k is some integer.Now, 2m equals 2kn + 2r. Hence, dividing 2m by 2n yields 2m/2n = (2kn + 2 r)/2n = k + 2r/2n. Since we are dividing by 2n (not by n), the remainder when divided by 2n is 2r.

    [b]My question : Why the remainder is 2r? I don't understand that part.[/b]

    2) If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of
    k + m ?

    a)6 b)7 c)8 d)9 e)10

    Answer is E


    Please help me out,guys. I would be very grateful if you guys could explain in detail.

    Thank you in advance.

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    Shalabh's Quants Really wants to Beat The GMAT!
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    Post Wed Apr 11, 2012 6:42 am
    shanice wrote:
    1) The remainder when positive integer m is divided by n is r. What is the remainder when 2m id divided by 2n?

    a)r b)2r c)2n d)m-nr e)2(m-nr)

    Answer is B.

    Explanation:
    Since the remainder when m is divided by n is r, we can represent m as m = kn + r, where k is some integer.Now, 2m equals 2kn + 2r. Hence, dividing 2m by 2n yields 2m/2n = (2kn + 2 r)/2n = k + 2r/2n. Since we are dividing by 2n (not by n), the remainder when divided by 2n is 2r.

    My question : Why the remainder is 2r? I don't understand that part.

    2) If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of
    k + m ?

    a)6 b)7 c)8 d)9 e)10

    Answer is E


    Please help me out,guys. I would be very grateful if you guys could explain in detail.

    Thank you in advance.
    Take an example Say m = 14 and n = 3. r = 2. Now 2m = 28 and 2n = 6. r = 4. Double.

    Q 1. What I understand that you wish to cancel 28 & 6 by 2 first and then calculate the remainder. In that case it gives a wrong impression as remainder equals 1.

    Now think like this.

    "You have 28 candies and you have to distribute equally to 6 children. How many will be left with you?" each will get 4 each and 4 will be left with you.

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    Post Wed Apr 11, 2012 6:59 am
    shanice wrote:
    1) The remainder when positive integer m is divided by n is r. What is the remainder when 2m id divided by 2n?

    a)r b)2r c)2n d)m-nr e)2(m-nr)

    Answer is B.

    Explanation:
    Since the remainder when m is divided by n is r, we can represent m as m = kn + r, where k is some integer.Now, 2m equals 2kn + 2r. Hence, dividing 2m by 2n yields 2m/2n = (2kn + 2 r)/2n = k + 2r/2n. Since we are dividing by 2n (not by n), the remainder when divided by 2n is 2r.

    My question : Why the remainder is 2r? I don't understand that part.

    2) If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of
    k + m ?

    a)6 b)7 c)8 d)9 e)10

    Answer is E


    Please help me out,guys. I would be very grateful if you guys could explain in detail.

    Thank you in advance.
    Q2. We can write this as...

    => 4242/100 = k(14 + m/50)
    .
    .
    .
    or reduce this to

    2121 = k (700 + m); by LCM and simplification.

    => 3*7*101 = k(700 + m); By factoring 2121. 101 is prime no.

    Say k =3 then 7*101 = 707 = 700 + m => m = 7

    Or K+n = 3+7 = 10.(Acceptable soln.)

    Say k =7 then 3*101 = 303 = 700 + m => m is negative. Not possible as m is +ive.

    Similarly k = 101 or 21 or 303 not possible.

    So only option left is k =3 & K+n = 3+7 = 10.

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    shanice Really wants to Beat The GMAT! Default Avatar
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    Post Wed Apr 11, 2012 7:44 am
    Thank you very much, Sir. You have been very helpful .

    LalaB GMAT Destroyer!
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    Post Wed Apr 11, 2012 8:43 am
    1) The remainder when positive integer m is divided by n is r. What is the remainder when 2m id divided by 2n?

    a)r b)2r c)2n d)m-nr e)2(m-nr)

    My approach-

    let m=3 n=5 then r=3
    so, if 2m=6(3*2) n=10(5*2) then R=6 (or 2r)

    ans is B

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    Post Wed Apr 11, 2012 9:35 am
    Thank you, LalaB

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    Post Wed Apr 11, 2012 10:00 am
    if the problem looks to be too simple, Respect it!!

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    Post Wed Apr 11, 2012 2:25 pm
    shanice wrote:
    Thank you very much, Sir. You have been very helpful .
    You are welcome Shanice. Don't forget to press Thank you Icon. Smile

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