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Re: If when x is divided by z, the result is y remainder q, then [#permalink]
10 Nov 2016, 15:47

Expert's post

Explanation

As soon as you see variables in the answer choices, set up your scratch paper to Plug In. If x = 16 and z = 5, then 16 ÷ 5 = 3 remainder 1, so y = 3 and q = 1. Plug your values into the answer choices, and only choice (B) works:

\(\frac{16}{5}-3=\frac{1}{5}\).

Hence option B is correct.
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Re: If when x is divided by z, the result is y remainder q, then [#permalink]
17 Nov 2016, 12:35

Expert's post

sandy wrote:

If when x is divided by z, the result is y remainder q, then which of the following must be true?

A. \(z(y + q) = x\) B. \(\frac{x}{z}-y=\frac{q}{z}\) C. \(xz - q = y\) D. \(\frac{x}{z}=y+q\) E. \(\frac{x}{z}=yz+q\)

There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

When x is divided by z, the result is y remainder q We can write: x = zy + q Check the answer choices....none of them match!

Looks like the question's author has taken x = zy + q and written an EQUIVALENT expression. So, we'll have to do the same to identify the correct answer.

Take x = zy + q Subtract zy from both sides to get: x - zy = q Divide both sides by z to get: x/z - zy/z = q/z Simplify to get: x/z - y = q/z Aha!!! Answer: