Bunuel
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
I would probably opt for
testing values for this question
Start with consecutive integers 1 and
21⁴ = 1 and 2⁴ = 16
Positive difference = 16 - 1 =
15Now check the answer choices...
(A) one less than twice the larger integer
2(
2) - 1 = 3
15 is divisible by 3
KEEP A
(B) one more than twice the larger integer
2(
2) + 1 = 5
15 is divisible by 5
KEEP B
(C) one less than four times the larger integer
4(
2) - 1 = 7
15 is NOT divisible by 7
ELIMINATE C
(D) one more than four times the larger integer
4(
2) + 1 = 9
15 is NOT divisible by 9
ELIMINATE D
(E) one more than eight times the larger integer
8(
2) + 1 = 17
15 is NOT divisible by 17
ELIMINATE E
We're left with A and B
Test another pair of consecutive integers
How about 2 and
32⁴ = 16 and 3⁴ = 81
Positive difference = 81 - 16 =
65(A) one less than twice the larger integer
2(
3) - 1 = 5
65 is divisible by 5
KEEP A
(B) one more than twice the larger integer
2(
3) + 1 = 7
65 is NOT divisible by 7
ELIMINATE B
Answer: A
Cheers,
Brent