## When the positive integer $$x$$ is divided by the positive integer $$y,$$ the quotient is $$3$$ and the remainder is $$z ##### This topic has expert replies Legendary Member Posts: 1668 Joined: 14 Oct 2017 Followed by:3 members ### When the positive integer \(x$$ is divided by the positive integer $$y,$$ the quotient is $$3$$ and the remainder is $$z by VJesus12 » Thu Apr 08, 2021 12:18 pm ## Timer 00:00 ## Your Answer A B C D E ## Global Stats When the positive integer \(x$$ is divided by the positive integer $$y,$$ the quotient is $$3$$ and the remainder is $$z.$$ When $$z$$ is divided by $$y,$$ the remainder is $$2.$$ Which of the following could be the value of $$x?$$

I. $$5$$
II. $$8$$
III. $$32$$

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Source: GMAT Club Tests

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### Re: When the positive integer $$x$$ is divided by the positive integer $$y,$$ the quotient is $$3$$ and the remainder is

by swerve » Fri Apr 09, 2021 5:36 pm
VJesus12 wrote:
Thu Apr 08, 2021 12:18 pm
When the positive integer $$x$$ is divided by the positive integer $$y,$$ the quotient is $$3$$ and the remainder is $$z.$$ When $$z$$ is divided by $$y,$$ the remainder is $$2.$$ Which of the following could be the value of $$x?$$

I. $$5$$
II. $$8$$
III. $$32$$

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Source: GMAT Club Tests
Here we have two equations,

$$\dfrac{x}{y}=3+z\quad$$ and $$\quad \dfrac{z}{y} = k+2$$

Now, let's start plugging in the options -

I. 5 - No possible satisfying conditions can be found out.
II. 8 - No possible satisfying conditions can be found out.
III. 32 - Let's try

$$\dfrac{32}{y}=3+z \quad \Longrightarrow \quad \dfrac{32}{9}=3(\text{Quotient})+5(\text{Remainder})$$

Let's try the second step now

$$\dfrac{z}{y}=k+2$$

$$\dfrac{5}{y}=k+2$$

$$\dfrac{5}{3}=1(\text{Quotient})+2(\text{Remainder})$$

Therefore, C

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