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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 which of

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Math Expert V
Joined: 02 Sep 2009
Posts: 60646
If when x is divided by z, the result is y remainder q, then which of  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 61% (01:18) correct 39% (01:04) wrong based on 102 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. $$\frac{x}{z}=yz+q$$

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

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$$Dividend = Divisor*Quotient + Remainder$$.

$$x = z*y + q$$
divide by z
$$\frac{x}{z} = y + \frac{q}{z}$$

moving y to LHS gives

$$\frac{x}{z} - y = \frac{q}{z}$$

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4228
Re: If when x is divided by z, the result is y remainder q, then which of  [#permalink]

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Top Contributor
Bunuel 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. $$\frac{x}{z}=yz+q$$

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"
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

Cheers,
Brent

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Target Test Prep Representative V
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Re: If when x is divided by z, the result is y remainder q, then which of  [#permalink]

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Bunuel 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. $$\frac{x}{z}=yz+q$$

We can create the equation:

x/z = y + q/z

x/z - y = q/z

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If when x is divided by z, the result is y remainder q, then which of   [#permalink] 15 Mar 2019, 06:40
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