Operatons on rational numbers

[carllecat]

I took this one from theQuant Sample Questions in the Diagnostic Test of OG11 (Question 13). The given explanation is not crystal clear and I am pretty sure some of you can give a better explanation.

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

The explanation:
The given equation can be written as 64.12t = s. By splitting portions of t into its integer multiple and its decimal multiple, this become 64t + 0.12 t = s, or 0.12t = s - 64t, which is the remainder. So, 0.12t = remainder. Test the answer choices to find the situation in which t is an integer.

A 0.12t = 2 or t = 16.67 NOT an integer
B 0.12t = 4 or t = 33.33 NOT an integer
C 0.12t = 8 or t = 66.67 NOT an integer
D 0.12t = 20 or t = 166.67 NOT an integer
E 0.12t = 45 or t = 375 INTEGER

Many thanks,

[DanaJ]

Check this out:

https://www.beatthegmat.com/og-number-props-t9935.html

[carllecat]

Check this out:

https://www.beatthegmat.com/og-number-props-t9935.html

Thanks a lot DanaJ!

[Ian Stewart]

I also posted a solution here, which might go into a bit more detail than the solution at the link above:

www.beatthegmat.com/difficult-t15709.html

[carllecat]

I also posted a solution here, which might go into a bit more detail than the solution at the link above:

www.beatthegmat.com/difficult-t15709.html

Thanks a lot Ian, you made it very clear.

Cheers!