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
Answer: C
Source: GMAT Club Tests
When the positive integer \(x\) is divided by the positive integer \(y,\) the quotient is \(3\) and the remainder is \(z
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Here we have two equations,VJesus12 wrote: ↑Thu Apr 08, 2021 12:18 pmWhen 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
Answer: C
Source: GMAT Club Tests
\(\dfrac{x}{y}=3+z\quad\) 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