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  Choose the correct choice:	A) I only	B) II only	C) III only	D) I and II only	E) I, II and III
When x is divided by y, the quotient is 3 and the remainder is z: x=3y+z, where 0≤z&lt;y (the remainder must be less than the divisor).   When z is divided by y, the remainder is 2: when divisor (y in our case) is more than dividend (z in our case), then the reminder equals to the dividend (for example, 2 divided by 5 gives the remainder of 2). Therefore, z=2 and 2&lt;y.   So, we have that x=3y+2 and 2&lt;y. This implies that the least value of x is x=3∗3+2=11: x cannot be 5 or 8.   Could x be 32? Yes. If y=10, then x=3∗10+2=32.   Answer: III only.
<result>C</result>
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