Number Properties, Remainders

[swerve]

What is the value of integer \(z?\)

1) \(z\) is the remainder when positive integer \(y\) is divided by positive integer \((y-1)\)
2) \(y\) is not a prime number

The OA is C

Source: Veritas Prep

[Ian Stewart]

When we divide y by y-1 in Statement 1, we'll get a quotient and remainder of 1 almost always, because y = (1)(y-1) + 1. There is only one exception: if y = 2, then when we divide by y - 1 = 1, we get a quotient of 2 and a remainder of 0, because that's the lone situation where y is divisible by y-1. So Statement 1 is very close to being sufficient, but we need Statement 2 to rule out the possibility that y = 2, and the answer is C (and z = 1).