If a and b are positive integers such that a/(4b) = 6.35, which of the following could be the remainder when 4a is divided by 2b?

Question

If a and b are positive integers such that a/(4b) = 6.35, which of the following could be the remainder when 4a is divided by 2b?
I. 10
II. 20
III. 40

Answer 1

(a/4b) = 6.35 and so a = 25.4b. Since a and b are integers it follows that b is a multiple of 5. (25.4 x 5 = 127)

Now, (4a/2b) =50.8. 

Thus 4a = 2b (50) + 2b (0.8). Now 4a and 2b (50) are integers where 50 is the quotient and 2b (0.8) is the remainder

  NOTE : Dividend = Divisor (quotient) + remainder       and the remainder is always less then the quotient

The remainder is always an integer and b is 5 or 10 or 15...…...

2b(0.8) is thus 8,16,24,32,40

 

Thus III is the only possibility.

Pradip