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

revised

64.12 = 64 + 12/100
s/t=64 + 12/100

we try only 12/100=answer choice/x, to see if x is integer
a.2 -> 12/100=2/x and x=200/12 bad
b.4 -> 12/100=4/x and x=400/12 bad
c.8 ... the same
d.20 is still bad
e.45 good as 12/100=45/x, 4/100=15/x and x=1500/4=375

choose e

arpitad 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

This should be quick

R/t=12/100=3/25

only 45 has 3 in it

So (E)

arpitad 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.