emmak wrote:

The positive difference of the fourth powers of two consecutive positive integers must be divisible by

(A) one less than twice the larger integer

(B) one more than twice the larger integer

(C) one less than four times the larger integer

(D) one more than four times the larger integer

(E) one more than eight times the larger integer

Using Picking Numbers for this, Let the two positive integers be 2, 3

\(3^4 - 2^4 = 81-16 = 65\)

(A) one less than twice the larger integer = 2(3) - 1 = 5 --> 65 is divisible by 5

(B) one more than twice the larger integer = 2(3) + 1 = 7 --> ruled out

(C) one less than four times the larger integer = 4(3) - 1 = 11 --> ruled out

(D) one more than four times the larger integer = 4(3) + 1 = 13 --> 65 is divisible by 13

(E) one more than eight times the larger integer = 8(3) + 1 = 25 --> ruled out

Another set of numbers, 3,4

\(4^4 - 3^4 = 256-81 = 175\)

(A) one less than twice the larger integer = 2(4) - 1 = 7 --> 175 is divisible by 7

(D) one more than four times the larger integer = 4(4) + 1 = 17 --> ruled out

Answer : A

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