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Number System
by Abhishek TG - Friday, 1 August 2014, 11:30 PM
  a number when divided by 6 leaves a remainder of +3,
when divided by 7 leaves a remainder of +1,
when divided by 11 leaves a remainder of +4.
find the general form of number ?
Re: Number System
by Raghav Lakhotia - Wednesday, 13 August 2014, 06:46 PM
  462k + 15 ?
Re: Number System
by Abhishek TG - Thursday, 21 August 2014, 11:52 AM
  HOW ?
Re: Number System
by TG Team - Friday, 22 August 2014, 12:22 PM
  Hi Abhishek smile

N = 6a + 3 = 7b + 1
i.e. 6a + 2 = 7b
i.e. 7b = 2(3a + 1) i.e. 3a + 1 must be multiple of 7, so smallest value of a which satisfy is 2.

Thus N = c*LCM(6, 7) + 6(2) + 3 = 42c + 15

ALso it is given that N = 11d + 4.

So 42c + 15 = 11d + 4
i.e. 11d = 42c + 11, so smallest value of c which satisfy this is c = 0

Thus N = k*LCM(11, 42) + 42(0) + 15 = 462k + 15. smile

Kamal Lohia