Data Sufficiency

If n>2 and n^4 - 5n^2 + 4 = 20h, is h an integer?

1) n/4 is an integer.
2) n/5 is an integer.

The OA is B.

Please, can anyone assist me with this DS question? I'm confused by it. Thanks in advance.

BTGmoderatorLU wrote:If n>2 and n^4 - 5n^2 + 4 = 20h, is h an integer?

1) n/4 is an integer.
2) n/5 is an integer.

n� - 5n² + 4 = 20h
(n²-4)(n²-1) = 20h
(n+2)(n-2)(n+1)(n-1) = 20h

h will be an integer if the left side is equal to a MULTIPLE OF 20.
Question stem, rephrased:
Is (n+2)(n-2)(n+1)(n-1) a multiple of 20?

Statement 1:
Test one case that also satisfies Statement 2.
Case 1: n=20, with the result that (n+2)(n-2)(n+1)(n-1) = 22*18*21*19.
Since 22*18*21*19 is not a multiple of 20, the answer to the rephrased question stem is NO.

Test one case that does NOT also satisfy Statement 2.
Case 2: n=4, with the result that (n+2)(n-2)(n+1)(n-1) = 6*2*5*3.
Since 6*2*5*3 is a multiple of 20, the answer to the rephrased question stem is YES.
Since the answer is NO in Case 1 buy YES in Case 2, INSUFFICIENT.

Statement 2:
Case 1 also satisfies Statement 2.
In Case 1, the answer to the rephrased question stem is NO.

Test one case that does not also satisfy Statement 1.
Case 3: n=5, with the result that (n+2)(n-2)(n+1)(n-1) = 7*3*6*4.
Since 7*3*6*4 is not a multiple of 20, the answer to the rephrased question stem is NO.

Cases 1 and 3 reveal that -- since n is a multiple of 5 -- none of the factors of (n+2)(n-2)(n+1)(n-1) will be a multiple of 5.
Since (n+2)(n-2)(n+1)(n-1) is not divisible by 5, it cannot be a multiple of 20.
Thus, the answer to the rephrased question stem is NO.
SUFFICIENT.

The correct answer is B.