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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If when x is divided by z, the result is y remainder q, then  Question banks Downloads My Bookmarks Reviews Important topics
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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Kudos [?]: 1865 , given: 397

If when x is divided by z, the result is y remainder q, then [#permalink]
Expert's post 00:00

Question Stats: 76% (01:10) correct 23% (01:27) wrong based on 21 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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Sandy
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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 112

Kudos [?]: 1865 , given: 397

Re: If when x is divided by z, the result is y remainder q, then [#permalink]
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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Sandy
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GRE Instructor Joined: 10 Apr 2015
Posts: 1802
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Kudos [?]: 1686 , given: 8

Re: If when x is divided by z, the result is y remainder q, then [#permalink]
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:
[Reveal] Spoiler:
B

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Intern Joined: 24 Oct 2017
Posts: 36
Followers: 0

Kudos [?]: 11 , given: 15

Re: If when x is divided by z, the result is y remainder q, then [#permalink]
this was tricky one
Intern Joined: 11 Jan 2018
Posts: 1
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Kudos [?]: 0 , given: 0

Re: If when x is divided by z, the result is y remainder q, then [#permalink]
you could try plugging in for the variables or apply the rule x=zy+q. So B is the answer
Manager Joined: 02 Jan 2018
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Kudos [?]: 32 , given: 0

Re: If when x is divided by z, the result is y remainder q, then [#permalink]
Answer is B.
Dividend= Divisor*Quotient+Remainder Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
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Kudos [?]: 79  , given: 99

Re: If when x is divided by z, the result is y remainder q, then [#permalink]
2
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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.

X/Z-Y =Q/Z hence the answer. 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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