Question

If \( s \) and \( t \) are positive integers such that \( \frac{s}{t} = 64.12 \), which of the following could be the remainder when \( s \) is divided by \( t \)?

• A. 2
• B. 4
• C. 8
• D. 16
• E. 20

Hint:

For division problems involving decimals, convert the decimal to a fraction and use it to find the remainder.

Answer 1

The Correct Option is C

Step 1: Express the given information.
We are given that \( \frac{s}{t} = 64.12 \), so we can express it as: \[ s = 64.12 \times t \] The number 64.12 has a fractional part of 0.12, so the remainder when \( s \) is divided by \( t \) should be \( 0.12 \times t \). \[ \text{Remainder} = 0.12 \times t \] Thus, \( t \) must be such that \( 0.12 \times t \) is an integer. The value of \( t \) can be 8, so the remainder is: \[ 0.12 \times 8 = 8 \] \[ \boxed{8} \]