Hades wrote:

Can a sequence of different positive integers \(X_{1}, X_{2}, X_{3}, . . . , X_{n}\) be ordered in such a way that the difference between any two consecutive integers is less than 2?

(1) Each term of the sequence has exactly 4 factors.

(2) \(X_{1}*X_{2}*X_{3}*...*X_{n-1}*X_{n}\) is divisible by \(2^{n}\)

In the highlighted part above, did you mean by

any two successive integers ?

If you say any consqcutive integers, then it is obviously yes but neither statement is required and D. If you meant "any two successive integers", then it is A.

(1) is suff. If each term of the sequence has exactly 4 factors, then obviously the difference between any two succesive integers is not <2.

(2) is not suff. To have the difference of < 2 (i.e. 1) between two succesive integers, the integers have to be consecutive.

* If n is even, then the difference could be 2 or >2. If n = 2, and x1 = 2 and x2 = 6, x1+x2 = 8, which is divisible nby 2^n.

* If n is odd, then the difference could be <2. If n = 3, x1 = 7, x2 =8 and x3 = 9, then x1+x2+x3 = 24, which is divisible by 2^n. NSF.

It is A.

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Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html

Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

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