Number system

Asked by ravikiran | 26th Aug, 2009, 09:02: PM

Expert Answer:

Let the number be x.

Case (1): When it is divided by 6 or 7 it leaves the remainder 1.

LCM of 6 & 7 = 42

Let say 'q' is the quotient obtained when the number is divided by 42.

So, we can write an equation as:

x = 42 x  q + 1............(1)

Case (2): When it is divided by 8or 11 it leaves the remainder 7.

LCM of 8 & 11 = 88

Let say 'r' is the quotient obtained when the number is divided by 88.

So, we can write an equation as:

x = 88 x  r + 1..................(2)

From 1 and 2, we have

21q = 3 + 44r

Now the equaion is true for integral value r = 9 and q = 19.

Therefore the number is x = 42 x 19 + 1= 799

So, the largest number is 799.

Answered by  | 27th Aug, 2009, 12:57: PM

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