Problem Solving

If s and t are positive integers 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

GMATGuruNY wrote:If s and t are positive integers 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

When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1.
Decimal representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = .5.
Since the two values are equal:
Remainder/divisor = decimal.

We should write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

In the problem above:
Remainder = R
Divisor = t
Decimal = .12 = 12/100 = 3/25.
Plugging these values into remainder/divisor = decimal, we get:
R/t = 3/25.

Since R/t is in its most reduced form, we know that t must be a multiple of 25 and that R must be a multiple of 3.
Only answer choice E is a multiple of 3.

The correct answer is E.

Its [E] 45..

Here is how my thought process goes-

s/t = 64.12
=> s = 64t + 0.12t

Here 64 is the quotient and 0.12t is the remainder.

0.12t => 3*t/75 => 3*(t/75)

Thus remainder is a multiple of 3, hence option [E] is the only choice possible!!