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If when x is divided by z, the result is y remainder q, then
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10 Nov 2016, 15:45
10 Nov 2016, 15:45
Expert Reply
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Question Stats:
79% (01:07) correct
20% (01:26) wrong based on 67 sessions
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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. \(\frac{x}{z}=yz+q\)
A. \(z(y + q) = x\)
B. \(\frac{x}{z}-y=\frac{q}{z}\)
C. \(xz - q = y\)
D. \(\frac{x}{z}=y+q\)
E. \(\frac{x}{z}=yz+q\)
Drill 3
Question: 13
Page: 292
Question: 13
Page: 292
Re: If when x is divided by z, the result is y remainder q, then
[#permalink]
10 Nov 2016, 15:47
10 Nov 2016, 15:47
Expert Reply
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.
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
17 Nov 2016, 12:35
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. \(\frac{x}{z}=yz+q\)
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:
Show: ::
B
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