Mistake? Number Properties, chapter 4, p86

[guy29]

There's an example given in the text, in the Number Prop. Guide on p86, that seems to be incorrect.

If x^3 - x = p, and x is odd, is p divisible by 24?

The example breaks down the equation into the following: (x-1)*x*(x+1)=p. The example claims that the answer is yes, because the formula shows a set of consecutive integers. But the question does not state that x is not 1, in which case they would not be consecutive integers, and p=0. Would that be correct?

Also, I'm not sure, but would the GMAT state that x is a nonnegative odd number or would that be assumed?

[esledge]

If x is 1, the integers x-1, x, and x+1 are still consecutive: 0, 1, and 2 are consecutive even though they are not all positive.

p = 0 is actually divisible by 24. In fact, zero is divisible by everything (except zero) because 0/n = 0, an integer.

To answer your question about the GMAT tendency--I suspect they would rule out this case somehow (perhaps "x is an odd integer greater than 2"), simply so that a correct answer tested divisibility rules more generally and didn't hinge on understanding of the more specific properties of zero.

However, this is a frequently asked question. Some other threads that mention the properties of zero:
http://www.manhattangmat.com/forums/is- ... -t171.html
http://www.manhattangmat.com/forums/pro ... t3410.html
http://www.manhattangmat.com/forums/rej ... t2510.html
http://www.manhattangmat.com/forums/num ... t4998.html

[guy29]

Oh I see, how silly of me to make that mistake. Thanks so much!

[esledge]

Glad to help!