Operations on Rational Numbers

[Jeevanantham]

If s and t are positive numbers 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.

Source : OG . Please explain the way to solve this problem. What is the key point in this problem to start up solving it.

[aneesh.kg]

If s and t are positive numbers 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.

Source : OG . Please explain the way to solve this problem. What is the key point in this problem to start up solving it.

Let's discuss a few concepts first.

Any number N can be represented by:
N = Divisor*Quotient + Remainder
Dividing LHS and RHS by Divisor,
(N/Divisor) = Quotient + (Remainder/Divisor)
(N/Divisor) = Integral Part + Decimal Part
Any number when divided by another number leaves an Integral Part and a Decimal Part. The Integral Part = Quotient whereas the Decimal Part = (Remainder)/(Divisor)

Lets return to this problem.
Decimal Part = 0.12 = (Remainder)/t
Remainder = 0.12t = 3t/25
The Remainder has to be a multiple of 3 (and 't' has to be a multiple of 25).

Among the options given, there is just one option that is a multiple of 3.
[spoiler](E)[/spoiler] is correct.

[Jeevanantham]

Thanks for your reply.

But How come 0.12t = 3t/25 ? I did not get this point alone.

[aneesh.kg]

Thanks for your reply.

But How come 0.12t = 3t/25 ? I did not get this point alone.

0.12t = 12t/100 = 3t/25
I'm sure you could've thought of that too

[Jeevanantham]

Yup... You made it simple... Thanks man..