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Bunuel
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If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3

If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3

If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3

Answer: C
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The sum of any three consecutive integer is divisible by 3 while their products is divisible by 6.
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Bunuel
The sum of 3 consecutive numbers is definitely:

A. Positive.
B. Divisible by 2.
C. Divisible by 3.
D. Divisible by 4.i
E. Divisible by 5.
Bunuel or anyone, suppose the consecutive NUMBERS are 1/4, 1/2, and 3/4?

Doesn't that qualify as an arithmetic sequence with common difference of 1/4?

If so, 1/4 + 2/4 + 3/4 = 6/4 or 3/2. 3/2 divided by 3 is 1/2.

The only answer that makes sense from the question is indeed C, but I had to decide that "number" meant "integer."

I see the word "number" and think, "It might be a trap."

As far as I understand it, the rule (sum of three consecutive integers always divisible by 3) only applies to integers.

What am I missing?
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Bunuel
The sum of 3 consecutive numbers is definitely:

A. Positive.
B. Divisible by 2.
C. Divisible by 3.
D. Divisible by 4.i
E. Divisible by 5.
Bunuel or anyone, suppose the consecutive NUMBERS are 1/4, 1/2, and 3/4?

Doesn't that qualify as an arithmetic sequence with common difference of 1/4?

If so, 1/4 + 2/4 + 3/4 = 6/4 or 3/2. 3/2 divided by 3 is 1/2.

The only answer that makes sense from the question is indeed C, but I had to decide that "number" meant "integer."

I see the word "number" and think, "It might be a trap."

As far as I understand it, the rule (sum of three consecutive integers always divisible by 3) only applies to integers.

What am I missing?

Consecutive numbers = consecutive integers. Agree it should be written more clearly in the question.
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Bunuel
The sum of 3 consecutive numbers is definitely:

A. Positive.
B. Divisible by 2.
C. Divisible by 3.
D. Divisible by 4.
E. Divisible by 5.

Lets sum a few consecutive numbers:

1 + 2 + 3 = 6

10 + 11 + 12 = 33

We see that the sum of 3 consecutive integers will always be divisible by 3.

Answer: C
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