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# If when x is divided by z, the result is y remainder q, then

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If when x is divided by z, the result is y remainder q, then [#permalink]  10 Nov 2016, 15:45
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Question Stats:

73% (01:14) correct 26% (01:27) wrong based on 19 sessions
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. $$\frac{x}{z}=yz+q$$

Drill 3
Question: 13
Page: 292
[Reveal] Spoiler: OA

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1731 [0], given: 397

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
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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!!!
[Reveal] Spoiler:
B

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Re: If when x is divided by z, the result is y remainder q, then [#permalink]  22 Jan 2018, 08:14
this was tricky one
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Re: If when x is divided by z, the result is y remainder q, then [#permalink]  22 Jan 2018, 10:26
you could try plugging in for the variables or apply the rule x=zy+q. So B is the answer
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Re: If when x is divided by z, the result is y remainder q, then [#permalink]  23 Jan 2018, 09:38
Dividend= Divisor*Quotient+Remainder
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Re: If when x is divided by z, the result is y remainder q, then [#permalink]  23 Apr 2018, 07:27
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We can also solve this question by using the following form of construct the divisor formular.

X/Z=Y+Q/Z

here simply

quotient Y is moved to the left hand side of the equation.

option B.

I got this question wrong but when I carefully read the option, option B was glaringly obvious.(patent answer)
Re: If when x is divided by z, the result is y remainder q, then   [#permalink] 23 Apr 2018, 07:27
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