x, y and z are consecutive positive integers such that x < y < z

It can sometimes be useful to know that the product of n consecutive integers is always divisible by n!. For example, if you have 3 consecutive integers, their product will always be divisible by 3! = 6. This is true because multiples of 3 are three apart, so among any three consecutive integers, you will always find you have exactly one multiple of 3. You'll also always have at least one multiple of 2, so the product of three consecutive integers must be divisible by 3*2. You can use the same logic to prove that the product of 4 consecutive integers is divisible by 4! = 24 (among any four consecutive numbers, you always have exactly one multiple of 4, at least one multiple of 3, and another number which is a multiple of 2), and so on.

If you know this, you can see instantly that (1) is true. Further, xy is the product of 2 consecutive integers so must be divisible by 2! = 2, and there is no way that (3) is true. As others did above, you can establish that (2) is true by substitution.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.