This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

We are given that x/y = 94.35. Using the remainder formula, we can say:

x/y = 95.35

x/y = 95 + 35/100

x/y = 95 + 7/20

We see that we now can equate 7/20 to r/y:

7/20= r/y

We see that the remainder must be a multiple of 7. The only answer choice that is not a multiple of 7 is 15.

Answer: B
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\(\frac{x}{y}=94.35.......x=94.35y=94y+0.35y\)..
So Remainder is 0.35y so remainder will be multiple of 7 as 35 is multiple of 7..

ONLY 15 in choices is not a multiple of 7...
Hence 15 cannot be the remainder

B

Can you please explain how you got 7/35?

7/35 should have actually been 7/20 since 35/100 = 7/20 . I've updated my solution.

Thank you for pointing that out!
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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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Asked: 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?

x/y = 94.35
R/y = .35 = 35/100 = 7/20
R should be a multiple of 7

IMO B

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