Source: Princeton Review
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. \(\frac{x}{z}=yz+q\)
The OA is B
If when x is divided by z, the result is y remainder q, then
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- Jay@ManhattanReview
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Let's take this question as: when 13 is divided by 3, the result is 4 and the remainder is 1.BTGmoderatorLU wrote:Source: Princeton Review
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. \(\frac{x}{z}=yz+q\)
The OA is B
Thus, 13 = 3*4 + 1
Coming to the question:
x = yz + q
There is no option as x = yz + q. Dividing by z, we get x/z = y + q/z => x/z - y = q/z
The correct answer: B
Hope this helps!
-Jay
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When it comes to remainders, there's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R"BTGmoderatorLU wrote:Source: Princeton Review
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. \(\frac{x}{z}=yz+q\)
The OA is B
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
GIVEN: when x is divided by z, the result (aka quotient) is y remainder is q
Applying the above rule, we get: x = zy + q .
Check the answer choices . . . x = zy + q is not there.
Looks like we need to rewrite the expression
Take: x = zy + q
Subtract yz 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
Answer: B
Cheers,
Brent