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22 Jan 2020, 02:33
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (02:07) correct
28%
(02:18)
wrong
based on 399
sessions
History
Date
Time
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Not Attempted Yet
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
(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
22 Jan 2020, 02:38
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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
(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
\((a+1)^4 - a^4\) = \([(a+1)^2 - a^2][(a+1)^2 + a^2]\) = \([(2a+1)][(a+1)^2 + a^2]\) = \([2(a+1) -1][(a+1)^2 + a^2]\)
2(a+1) -1 = one less than twice the larger integer
Answer: Option A
19 Sep 2020, 07:47
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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
(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 2
1⁴ = 1 and 2⁴ = 16
Positive difference = 16 - 1 = 15
Now 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 3
2⁴ = 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
