Bunuel wrote:

If x and y are integers, then \(\frac{x(x + 1)(x + 2)}{2*3*5^y}\) must be an integer if which of the following is true ?

A. x is even.

B. x is odd.

C. x is divisible by three.

D. y is even.

E. y is equal to zero.

Questions dealing with number properties can often be solved with logic and very little calculation.

We'll look for such a solution, a Logical approach.

A fraction is an integer if its numerator is divisible by its denominator.

So, our correct answer must either say that the numerator is 0 (as 0 divided by any number is 0) or have some information about the denominator, that is about y. (Otherwise y could be any number, and specifically one that is not a factor of the numerator)

(A), (B), (C) are eliminated.

(D) is also insufficient as we can just increase y until we find a power of 5 that is not a factor of x(x+1)(x+2).

(E) must be our answer.

We can mark it, if we have the time we'll also see why it is true: x(x+1)(x+2) are 3 consecutive numbers and therefore at least one of them is even and one must be divisible by 3. So they are definitely divisible by 2*3 and since y = 0 means 5^y = 1, (E) is correct.

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