Bunuel wrote:

For positive integers x and y, x/y=94.35. Which of the following could not be the remainder when x is divided by y?

A. 14

B. 15

C. 35

D. 70

E. 105

OFFICIAL EXPLANATION

This theoretical remainder problem is essentially testing you on whether you can determine the relationship between the remainder (what they're asking you for) and the decimals in the result of a division problem.

To illustrate that relationship, consider an easy problem like "what is 7 divided by 4?"

You could answer that three different ways. If you wanted to use a remainder, you'd say 1, remainder 3. If you wanted to use a mixed number, you'd say 1 and 3/4. And if you wanted to use decimals, you'd divide that remainder of 3 by the 4 (like you have in your mixed number) and get to 1.75.

What does that tell you about the relationship between remainder and decimal? The remainder divided by the divisor gives you the decimal places. Here, that means that the remainder divided by y must equal 0.35. Mathematically, that looks like:

r/y=35/100, since "0.35" means "thirty-five one-hundredths." If you reduce that fraction on the right, you should see that \(\frac{r}{y}=\frac{7}{20}\). Since you know that both r and y must be integers, then r must be a multiple of 7, and y must be a multiple of 20. As you scan the answer choices for possible values of r, 15 should stand out as the only number that's not a multiple of 7, making 15 the correct answer.

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