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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
51% (01:22) correct
49%
(01:18)
wrong
based on 253
sessions
History
Date
Time
Result
Not Attempted Yet
The sum of four consecutive odd integers must be:
A. even, but not necessarily divisible by 4
B. divisible by 4, but not necessarily by 8
C. divisible by 8, but not necessarily by 16
D. divisible by 16
E. None of the above
A. even, but not necessarily divisible by 4
B. divisible by 4, but not necessarily by 8
C. divisible by 8, but not necessarily by 16
D. divisible by 16
E. None of the above
27 Jul 2022, 03:27
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Cannot seem to get my head across the OA for this one. Any set of consecutive odd integers if you have a look have a sum which increases by 8 for example:
1,3,5,7 = 16
3,5,7,9 = 24
5,7,9,11 = 32 and so on
-5,-3,-1,1 = -8
-3,-1,1,3 = 0
So all should be multiples of 4, should be multiples of 8 because incrementing by 8 but not of 16
Thought the answer should be C
27 Jul 2022, 03:41
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Say the four consecutive odd integers are \((2k - 3); \ (2k - 1); \ (2k +1); \ and \ (2k + 3)\), for some integer k.
The sum will be: \((2k - 3) + (2k - 1) + (2k + 1) + (2k + 3) = 8k\).
So, the sum of four consecutive odd integers is always a multiple of 8 (so it's also even and a multiple of 4).
A. even, but not necessarily divisible by 4 --> NOT true.
B. divisible by 4, but not necessarily by 8 --> NOT true.
C. divisible by 8, but not necessarily by 16 --> TRUE.
D. divisible by 16 --> NOT true.
E. None of the above
Answer: C.
