Mike@Magoosh wrote:If n is an integer greater than 50, then the expression (n^2 - 2n)(n^2 - 1) MUST be divisible by which of the following?
I. 4
II. 6
III. 18
(A) I only
(B) II only
(C) I & II only
(D) II & III only
(E) I, II, and III
(n² - 2n)(n² - 1) = n(n-2)(n+1)(n-1) = (n-2)(n-1)(n)(n+1).
(n-2)(n-1)(n)(n+1) is the product of four consecutive integers.
Of every 4 consecutive integers, at least one will be a MULTIPLE OF 3 and exactly one will be a MULTIPLE OF 4.
Thus, the product of four consecutive integers must be a MULTIPLE OF 12.
Implication:
Statements I and II must be true.
Eliminate any answer choice that does not include both I and II (A, B and D).
If n=51, then (n-2)(n-1)(n)(n+1) = 49*50*51*52 = (7*7)(2*5*5)(3*17)(2*2*13).
The resulting product is not divisible by 18.
Eliminate any remaining answer choice that includes statement III (E).
The correct answer is
C.
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