Remainder

If a number x is divided by another number y and the result is 102.15, then the remainder when x is divided by y is 0.15y.

Also understand that the smallest possible natural number of the form 0.15y is 3; so our resulting remainder must be a multiple of 3. Among the answer options only 42 is a multiple of 3 and hence the answer.

If x is divided by y and the result is 120.15, which of the following could be the remainder of x/y?

28
42
58
88
92

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 = y
Decimal = .15 = 15/100 = 3/20.
Plugging these values into remainder/divisor = decimal, we get:
R/y = 3/20.

Since R/y is in its most reduced form, we know that y must be a multiple of 20 and that R must be a multiple of 3.
Only answer choice B is a multiple of 3.

The correct answer is B.

For a similar problem in the OG13, check here:

https://www.beatthegmat.com/remainder-t111428.html

Thanks a lot GMATGuruNY for giving the link for practising.